DIMACS benchmark set
This is a selected set of instances form the Second DIMACS Implementation Challenge (1992-1993).
In the following table, the clique number ω(G) corresponds to the global optimum or to the lower bound as indicated by the instance generator.
For some instances the lower bound has been confirmed to coincide with the global optimum. For such instances, the clique number is followed by a *.
The exact algorithms that confirmed the bound are reported later on this page.
| Instance | ω(G) | Best known | Nodes | Edges | Graph degrees | Best degrees |
|---|
| Median | IQR | Median | IQR |
|---|
| C125.9 | 34* | 34 | 125 | 6 963 | 112.0 | (5.00) | 114.5 | (4.75) |
| C250.9 | 44* | 44 | 250 | 27 984 | 224.0 | (6.00) | 227.0 | (5.00) |
| C500.9 | ≥ 57 | 57 | 500 | 112 332 | 449.0 | (9.00) | 455.0 | (9.00) |
| C1000.9 | ≥ 68 | 68 | 1 000 | 450 079 | 900.0 | (13.00) | 907.0 | (11.25) |
| C2000.9 | ≥ 80 | 80 | 2 000 | 1 799 532 | 1 800.0 | (18.00) | 1 803.0 | (15.25) |
| DSJC1000_5 | 15 | 15 | 1 000 | 499 652 | 500.0 | (20.00) | 503.0 | (23.00) |
| DSJC500_5 | 13 | 13 | 500 | 125 248 | 250.0 | (16.00) | 259.0 | (14.00) |
| C2000.5 | 16* | 16 | 2 000 | 999 836 | 999.0 | (30.00) | 1 006.0 | (11.50) |
| C4000.5 | 18* | 18 | 4 000 | 4 000 268 | 2 001.0 | (42.00) | 2 002.0 | (40.75) |
| MANN_a27 | 126 | 126 | 378 | 70 551 | 374.0 | (0.00) | 374.0 | (0.00) |
| MANN_a45 | 345 | 345 | 1 035 | 533 115 | 1 031.0 | (0.00) | 1 031.0 | (0.00) |
| MANN_a81 | 1 100* | 1 100 | 3 321 | 5 506 380 | 3 317.0 | (0.00) | 3 317.0 | (0.00) |
| brock200_2 | 12 | 12 | 200 | 9 876 | 99.0 | (10.00) | 101.0 | (11.00) |
| brock200_4 | 17 | 17 | 200 | 13 089 | 131.0 | (8.00) | 134.0 | (6.00) |
| brock400_2 | 29 | 29 | 400 | 59 786 | 299.0 | (10.00) | 299.0 | (9.00) |
| brock400_4 | 33 | 33 | 400 | 59 765 | 299.0 | (11.00) | 299.0 | (9.00) |
| brock800_2 | 24 | 24 | 800 | 208 166 | 521.0 | (18.00) | 516.5 | (20.25) |
| brock800_4 | 26 | 26 | 800 | 207 643 | 519.0 | (18.25) | 512.0 | (20.25) |
| gen200_p0.9_44 | 44 | 44 | 200 | 17 910 | 180.0 | (8.00) | 179.5 | (4.25) |
| gen200_p0.9_55 | 55 | 55 | 200 | 17 910 | 179.0 | (7.25) | 179.0 | (5.50) |
| gen400_p0.9_55 | 55 | 55 | 400 | 71 820 | 360.0 | (13.25) | 359.0 | (6.00) |
| gen400_p0.9_65 | 65 | 65 | 400 | 71 820 | 361.0 | (14.00) | 359.0 | (9.00) |
| gen400_p0.9_75 | 75 | 75 | 400 | 71 820 | 359.0 | (13.00) | 359.0 | (8.00) |
| hamming10-4 | 40 | 40 | 1 024 | 434 176 | 848.0 | (0.00) | 848.0 | (0.00) |
| hamming8-4 | 16 | 16 | 256 | 20 864 | 163.0 | (0.00) | 163.0 | (0.00) |
| keller4 | 11 | 11 | 171 | 9 435 | 110.0 | (8.00) | 112.0 | (17.00) |
| keller5 | 27 | 27 | 776 | 225 990 | 578.0 | (38.00) | 578.0 | (33.00) |
| keller6 | ≥ 59 | 59 | 3 361 | 4 619 898 | 2 724.0 | (50.00) | 2 724.0 | (50.00) |
| p_hat300-1 | 8 | 8 | 300 | 10 933 | 73.0 | (39.00) | 103.0 | (20.00) |
| p_hat300-2 | 25 | 25 | 300 | 21 928 | 146.5 | (73.00) | 213.0 | (18.00) |
| p_hat300-3 | 36 | 36 | 300 | 33 390 | 224.0 | (38.00) | 251.0 | (15.25) |
| p_hat700-1 | 11 | 11 | 700 | 60 999 | 174.5 | (87.00) | 250.0 | (22.50) |
| p_hat700-2 | 44 | 44 | 700 | 121 728 | 353.0 | (177.50) | 508.0 | (31.50) |
| p_hat700-3 | 62* | 62 | 700 | 183 010 | 526.0 | (89.00) | 602.0 | (14.00) |
| p_hat1500-1 | 12 | 12 | 1 500 | 284 923 | 383.0 | (197.00) | 509.0 | (82.00) |
| p_hat1500-2 | 65* | 65 | 1 500 | 568 960 | 763.0 | (387.00) | 1 100.0 | (37.00) |
| p_hat1500-3 | 94* | 94 | 1 500 | 847 244 | 1 132.5 | (192.00) | 1 297.5 | (25.75) |
The instances can be downloaded from the DIMACS ftp site, or directly from here. Archives containing the whole dataset and the selected instances are available below.
Instance families and generators
Below a brief description mostly cut-and-pasted from the headers of the instance files. Much more details about the instances can be found in the headers, in the README files of the generators, and in the linked papers.
C family
Random graphs: Cx.y, where x is the number of nodes and y the edge probability. These instances have been generated by Michael Trick using ggen, a program by Craig Morgenstern. DSJC family
Random graphs generated by David Johnson; more details available in Johnson et al. MANN family
Clique formulation of the Steiner Triple Problem, translated from the set covering formulation. Instances generated by Carlo Mannino. brock family
Random graphs with cliques hidden among nodes that have a relatively low degree. Instances generated by Mark Brockington and Joe Culberson; see Brockington et al. gen family
Artificially generated graphs with large, known embedded clique. Instances generated by Laura Sanchis. hamming family
Hamming graphs generated by Panos Pardalos. hamminga-b are graphs on a-bit words with an edge if and only if the two words are at least hamming distance b apart. keller family
Instances based on Keller's conjecture on tilings using hypercubes. These instances have been generated by Peter Shor; more details available in Lagarias et al., and Corrádi et al. p_hat family
Random graphs are generated with the p-hat generator which is a generalization of the classical uniform random graph generator. Graphs generated with p-hat have wider node degree spread and larger cliques than uniform graphs. These instances have been generated by Patrick Soriano and Michel Gendreau.
Recent new optima
- 2011 - Mascia et al. is the first algorithm for Maximum Clique to find a new best clique of size 1100 for MANN_a81.
- 2007 - Grosso et al. is the first algorithm for Maximum Clique to find a new best clique of size 80 for C2000.9.
Bounds confirmed by exact algorithms
The following instance bounds have been confirmed to be optimal by exact algorithms. The list of algorithms below is not exhaustive, and in some cases it could be that the exact algorithms reported are not the first ones to have confirmed the bounds. The list of references in this section is updated every time someone brings to my attention that a bound has been confirmed by a particular algorithm.
- C125.9 bound confirmed to be optimal with Cliquer.
- C250.9 bound confirmed to be optimal by Li et al. using MaxCLQ, which is available here.
- C2000.5 bound confirmed to be optimal with Cliquer.
- C4000.5 bound confirmed to be optimal by Xiang et al.
- MANN_a81 bound confirmed to be optimal by McCreesh et al.
- p_hat700-3 bound confirmed to be optimal by Li et al. using MaxCLQ, which is available here.
- p_hat1000-3 bound confirmed to be optimal by Li et al. using MaxCLQ, which is available here.
- p_hat1500-2 bound confirmed to be optimal by Li et al. using MaxCLQ, which is available here.
- p_hat1500-3 bound confirmed to be optimal by McCreesh et al.
Instances
If you have found other cliques or improved the best known solution, please let me know, so that I can update this page.
C125.9
Graph with 125 nodes, 6 963 edges, and ω(G)34*.Best-known
solution hassize 34.
Clique 1
7 9 11 13 19 22 25 29 33 34 40 44 49 52 54 55 66 67 68 70 79 80 93 96 98 99 103 104 110 111 114 117 122 125 C250.9
Graph with 250 nodes, 27 984 edges, and ω(G)44*.Best-known
solution hassize 44.
Clique 1
3 8 21 26 30 31 34 37 41 45 58 63 70 72 84 87 90 92 96 97 99 122 129 131 136 138 147 152 161 162 163 165 177 183 186 191 197 203 207 212 214 227 235 241 C500.9
Graph with 500 nodes, 112 332 edges, and ω(G)≥ 57.Best-known
solution hassize 57.
Clique 1
21 22 33 40 46 61 63 87 97 110 121 122 132 137 155 179 181 182 186 189 193 194 203 212 223 244 248 249 253 266 280 290 294 310 316 319 327 329 340 350 351 357 373 374 375 381 390 395 404 405 411 415 463 478 490 491 497 C1000.9
Graph with 1 000 nodes, 450 079 edges, and ω(G)≥ 68.Best-known
solution hassize 68.
Clique 1
17 24 44 53 58 67 97 106 119 146 162 167 191 196 201 213 241 250 265 266 278 284 285 308 319 327 339 346 351 398 431 442 456 475 494 564 572 574 579 582 585 598 613 628 637 638 656 674 679 683 684 721 735 736 743 777 783 796 799 808 845 872 886 914 941 951 962 994 C2000.9
Graph with 2 000 nodes, 1 799 532 edges, and ω(G)≥ 80.Best-known
solution hassize 80.
Clique 1
7 19 55 102 110 114 124 169 199 212 248 263 326 329 334 342 387 412 457 474 521 545 563 564 590 641 646 667 678 679 719 720 734 755 759 775 793 797 824 838 867 937 945 958 973 976 1001 1023 1048 1111 1117 1118 1137 1152 1223 1285 1286 1318 1338 1391 1424 1436 1489 1504 1521 1566 1598 1628 1717 1729 1740 1773 1797 1829 1841 1875 1883 1903 1917 1999 DSJC1000_5
Graph with 1 000 nodes, 499 652 edges, and ω(G)= 15.Best-known
solution hassize 15.
Clique 1
53 122 158 232 416 424 463 468 505 511 526 748 768 805 902 DSJC500_5
Graph with 500 nodes, 125 248 edges, and ω(G)= 13.Best-known
solution hassize 13.
Clique 1
4 60 89 122 132 313 359 396 425 448 455 468 480 C2000.5
Graph with 2 000 nodes, 999 836 edges, and ω(G)16*.Best-known
solution hassize 16.
Clique 1
157 208 355 416 492 581 701 809 1343 1574 1612 1662 1679 1782 1934 1993 C4000.5
Graph with 4 000 nodes, 4 000 268 edges, and ω(G)18*.Best-known
solutions havesize 18.
Clique 1
1 275 541 895 1159 1213 1326 1581 1669 1767 2125 2180 2743 2900 3414 3612 3842 3958 Clique 2
3 89 149 265 796 980 986 1145 1355 1428 1636 2063 2380 2713 3017 3210 3267 3331 Clique 3
8 128 448 661 711 972 1043 1370 1995 2277 2310 2479 2632 2750 3063 3648 3739 3754 Clique 4
25 423 488 494 498 883 1074 1076 1154 1326 2052 2296 2552 2659 2952 3191 3618 3645 Clique 5
23 137 390 578 800 835 1106 1332 1523 1890 1938 2668 2744 2893 2924 3645 3782 3809 Clique 6
35 308 658 724 830 1035 1095 2068 2336 2571 2874 3150 3199 3267 3424 3491 3587 3847 Clique 7
38 137 742 883 944 1021 1058 1422 1480 1483 1665 2049 2281 2353 2649 3206 3795 3838 Clique 8
41 219 305 808 886 1241 1430 1519 1728 1742 2404 2701 2717 3039 3155 3233 3819 3822 Clique 9
53 289 468 721 831 1070 1680 1919 2097 2133 2192 2600 2674 3393 3420 3709 3903 3974 Clique 10
61 207 633 1253 1708 1771 1819 2128 2427 2745 2805 2998 3021 3163 3202 3550 3571 3841 Clique 11
61 90 243 564 636 1098 1861 1889 2037 2044 2640 3027 3110 3180 3433 3619 3879 3965 Clique 12
75 120 148 274 330 727 940 1616 1923 2282 2307 2493 2674 2700 2870 3090 3190 3489 Clique 13
82 449 777 939 1316 1330 1450 1588 1964 2279 2385 2525 2685 2953 3080 3096 3128 3528 Clique 14
88 188 231 1007 1162 1417 1701 2139 2283 2407 2537 2688 2750 2903 3066 3073 3121 3855 Clique 15
92 149 249 528 567 701 1029 1228 1237 1926 2553 2580 3130 3244 3465 3659 3838 3932 Clique 16
96 591 690 1006 2246 2318 2392 2822 2840 2927 3172 3450 3507 3563 3715 3730 3909 3999 Clique 17
98 101 325 528 1203 1579 1856 2307 2517 2551 2752 2887 2981 3018 3536 3744 3811 3988 Clique 18
103 109 605 652 659 1143 1712 1760 1986 2056 2515 2810 2825 2866 3358 3507 3570 3741 Clique 19
105 247 928 930 1080 1163 1521 2015 2102 2591 2593 2845 3002 3021 3093 3368 3603 3916 Clique 20
105 484 1319 1687 1961 2299 2313 2342 2512 2609 2916 2936 3070 3283 3315 3333 3458 3852 Clique 21
110 226 307 548 661 833 1040 1071 1090 1160 1228 1721 1849 2998 3109 3317 3667 3899 Clique 22
135 301 1269 1566 1592 1875 1928 2049 2403 2505 2963 3084 3212 3347 3541 3664 3686 3816 Clique 23
153 389 460 827 858 2015 2172 2447 2703 2787 2808 2827 3210 3729 3830 3954 3961 3988 Clique 24
163 264 835 1012 1116 1430 1905 2024 2026 2141 2254 2475 2897 2958 3035 3183 3559 3695 Clique 25
166 228 472 518 836 859 1035 1407 1971 2120 2777 3105 3265 3366 3598 3645 3669 3907 Clique 26
176 196 343 471 664 669 700 1041 1151 1598 1723 1978 2221 2513 2685 3227 3474 3981 Clique 27
190 918 1056 1058 1100 1234 1355 1820 1984 1987 2122 2259 3142 3201 3221 3355 3579 3861 Clique 28
193 223 246 317 406 413 749 1797 1817 2065 2193 2414 2611 2955 3104 3578 3611 3772 Clique 29
203 300 448 465 524 734 923 947 1033 1332 1390 1686 2028 2891 2986 3167 3410 3497 Clique 30
211 308 832 890 1040 1228 1289 1526 1579 2149 2256 2328 3285 3369 3452 3464 3474 3824 Clique 31
233 379 414 707 927 1006 1449 1452 1518 1714 1804 2230 2244 2662 3153 3337 3507 3568 Clique 32
234 441 561 824 825 1053 1193 1307 2182 2278 2333 2358 2610 3100 3121 3537 3610 3921 Clique 33
240 252 353 897 935 937 1116 1275 2177 2189 2497 3131 3379 3628 3696 3781 3819 3846 Clique 34
246 511 639 935 994 1068 1252 1321 1577 1758 1826 1921 2094 2619 2883 2969 3121 3335 Clique 35
247 572 1138 1494 1718 1824 2245 2412 2640 2700 2806 2903 3341 3383 3415 3446 3567 3782 Clique 36
249 364 488 547 641 647 736 1065 1239 1347 1366 1593 1648 3089 3216 3607 3832 3903 Clique 37
303 1146 1147 1178 1381 1412 2008 2136 2341 2395 2667 3022 3055 3112 3394 3516 3750 3814 Clique 38
319 647 736 1098 1256 1344 1856 2106 2257 2453 2496 2636 2777 2787 2948 3390 3614 3718 Clique 39
340 354 647 760 845 1013 1047 1065 1132 1202 1656 1682 1892 1982 2550 2962 3227 3508 Clique 40
368 419 486 692 855 1316 1555 1952 2017 2172 2228 2457 2518 2658 3407 3833 3912 3999 Clique 41
401 554 796 1334 1355 1465 1573 1740 1779 1809 1876 2099 2412 2442 2678 3149 3168 3512 Clique 42
560 648 696 933 1139 1397 1400 1617 1659 2287 2424 2685 2741 2955 3275 3277 3450 3780 Clique 43
625 800 824 830 1026 1080 1114 1364 1396 1964 2526 2673 2992 3093 3575 3689 3769 3849 Clique 44
1170 1236 1267 1317 1363 1604 1774 2063 2373 2479 2536 2539 3038 3158 3294 3307 3757 3970 MANN_a27
Graph with 378 nodes, 70 551 edges, and ω(G)= 126.Best-known
solution hassize 126.
Clique 1
2 3 4 6 13 19 21 24 25 28 32 35 37 40 45 48 51 53 55 59 63 65 69 71 75 77 79 82 87 88 91 94 98 101 103 108 111 114 115 118 122 125 128 130 135 137 140 143 145 148 153 155 159 161 163 167 170 172 176 179 181 184 188 191 194 198 199 203 206 209 211 216 217 221 224 227 230 232 236 239 243 245 247 251 253 257 260 264 266 268 272 274 278 282 285 286 290 293 296 299 303 306 308 311 313 317 321 323 326 329 333 335 337 341 343 348 350 352 356 359 363 364 368 371 374 377 MANN_a45
Graph with 1 035 nodes, 533 115 edges, and ω(G)= 345.Best-known
solutions havesize 345.
Clique 1
11 12 13 14 15 21 22 23 24 25 41 42 43 44 45 47 50 53 57 60 62 65 68 71 75 77 80 83 86 89 92 95 98 101 104 106 109 112 115 118 121 124 127 130 133 136 139 142 146 148 151 155 157 160 164 167 170 173 175 178 183 186 189 192 195 198 201 204 207 210 213 215 217 221 223 226 230 234 237 240 241 244 247 252 255 258 260 263 266 268 272 274 277 281 283 286 290 292 295 299 301 304 307 310 313 316 319 322 325 328 331 334 337 340 343 347 349 353 355 358 363 364 369 371 374 378 380 384 386 389 391 394 397 400 403 406 409 412 415 418 421 425 428 430 433 436 439 442 445 448 451 454 457 460 463 468 471 474 477 478 483 486 487 492 495 497 499 504 506 510 512 516 519 521 524 527 529 533 535 538 542 544 548 550 554 558 559 564 566 568 572 574 577 581 585 586 590 592 595 598 601 604 607 610 613 616 619 622 625 628 632 635 638 641 644 647 650 653 656 659 662 665 668 670 673 676 679 682 687 690 691 696 699 700 703 706 709 712 716 720 721 726 727 731 733 737 741 744 747 750 753 756 758 762 764 768 771 774 776 778 782 786 789 790 793 798 800 804 807 808 813 816 819 822 825 828 831 834 837 840 842 845 848 851 854 857 860 863 866 869 873 876 878 881 884 888 891 894 895 898 903 905 909 910 913 918 921 924 927 930 933 936 939 942 945 948 950 954 957 960 963 966 969 972 975 978 981 984 987 990 993 996 998 1000 1003 1008 1011 1014 1015 1018 1022 1025 1028 1031 1034 Clique 2
11 12 13 14 15 26 27 28 29 30 36 37 38 39 40 46 50 53 57 60 62 65 69 72 75 77 79 83 85 89 92 94 98 101 104 106 109 112 115 118 121 124 127 130 133 137 140 142 146 149 151 156 158 161 164 166 170 173 175 179 182 185 188 191 193 196 199 202 206 208 211 214 217 220 223 226 229 232 235 238 241 245 247 250 254 257 260 262 265 268 271 274 277 281 283 288 291 294 297 300 303 306 309 312 315 316 319 323 326 328 331 334 339 340 343 346 349 352 357 358 362 365 368 371 374 377 380 383 385 389 393 394 398 401 405 408 411 414 417 418 423 426 427 432 433 438 441 444 447 450 453 455 457 462 464 468 470 474 477 479 483 485 489 492 494 496 499 502 505 508 511 514 517 520 523 528 531 534 537 538 543 546 547 552 555 556 559 562 565 568 572 575 577 581 584 587 589 593 596 599 601 604 607 612 614 617 621 622 627 628 633 635 638 641 645 648 650 653 656 660 663 665 668 670 673 678 680 684 687 690 693 696 699 700 705 706 709 712 715 718 721 724 727 730 733 738 741 744 747 750 753 756 759 762 765 768 771 774 775 780 782 786 789 790 794 798 801 803 806 808 812 815 818 821 824 827 830 833 836 839 843 846 848 852 855 858 861 863 866 870 872 875 878 881 884 887 891 894 897 899 903 905 909 910 915 917 920 923 926 929 932 935 938 941 944 948 951 954 957 960 963 966 969 972 975 978 981 984 987 990 993 996 998 1001 1005 1006 1010 1012 1015 1018 1023 1026 1029 1032 1035 MANN_a81
Graph with 3 321 nodes, 5 506 380 edges, and ω(G)1 100*.Best-known
solution hassize 1 100.
Clique 1
2 3 4 6 20 21 25 26 31 44 46 47 49 53 55 57 60 61 69 79 82 86 88 91 94 99 102 105 107 109 113 117 118 123 125 127 131 134 137 141 143 145 150 152 154 159 162 164 167 170 173 176 179 181 185 188 190 195 197 199 203 206 209 212 215 217 221 224 226 230 232 235 240 243 246 249 252 253 258 261 263 267 268 272 275 279 281 284 286 290 292 296 300 302 304 307 312 314 317 320 322 327 328 332 335 339 341 345 348 351 354 357 360 362 366 369 372 375 377 381 383 386 389 392 395 399 401 404 406 410 413 417 420 423 424 428 431 435 438 440 443 446 450 452 456 458 460 464 467 469 474 475 478 481 484 488 491 494 496 500 503 507 509 513 516 518 522 524 526 529 534 536 538 543 545 549 551 554 558 560 562 566 568 572 575 577 581 583 586 589 592 596 598 602 605 609 610 614 616 619 622 625 630 631 635 637 641 643 646 649 652 655 658 661 665 667 672 673 677 679 682 686 688 692 695 697 700 704 706 711 713 715 718 721 724 727 731 733 736 740 742 746 748 751 755 758 761 763 767 769 772 776 778 783 785 787 792 795 798 800 802 806 809 812 815 819 820 823 826 829 832 835 838 842 846 847 850 855 856 859 864 865 868 872 874 878 881 883 887 891 893 895 900 903 906 909 910 915 917 920 924 927 930 931 936 939 942 945 947 951 954 957 960 962 965 967 972 974 977 979 983 985 988 992 995 999 1002 1005 1007 1011 1014 1015 1019 1021 1025 1027 1032 1034 1037 1041 1043 1046 1049 1053 1055 1059 1062 1064 1068 1069 1074 1077 1078 1083 1086 1089 1092 1094 1098 1101 1104 1105 1109 1112 1116 1117 1122 1125 1127 1131 1134 1135 1139 1142 1145 1148 1152 1154 1158 1160 1162 1166 1169 1171 1175 1179 1180 1184 1188 1190 1192 1197 1200 1202 1205 1207 1210 1215 1218 1221 1224 1226 1230 1232 1234 1239 1242 1243 1247 1251 1254 1255 1260 1262 1266 1268 1270 1275 1278 1279 1284 1287 1290 1291 1296 1298 1302 1305 1308 1311 1314 1316 1318 1323 1325 1328 1332 1334 1338 1339 1343 1347 1350 1353 1356 1357 1362 1365 1368 1371 1374 1376 1380 1383 1385 1388 1392 1395 1397 1400 1404 1406 1410 1413 1415 1419 1422 1425 1428 1429 1434 1437 1440 1442 1444 1448 1452 1455 1457 1461 1464 1467 1470 1473 1475 1478 1482 1485 1486 1490 1493 1495 1499 1503 1505 1509 1512 1515 1517 1520 1524 1526 1528 1531 1534 1539 1541 1545 1547 1549 1552 1555 1560 1563 1566 1569 1570 1575 1578 1581 1584 1587 1590 1592 1594 1598 1601 1603 1606 1610 1613 1617 1619 1621 1626 1628 1630 1634 1638 1639 1642 1647 1650 1653 1656 1657 1661 1665 1668 1669 1674 1677 1680 1683 1686 1689 1690 1695 1698 1700 1704 1705 1710 1711 1716 1719 1722 1724 1728 1731 1732 1736 1740 1743 1746 1749 1752 1755 1758 1759 1762 1767 1770 1772 1776 1779 1781 1785 1786 1791 1792 1796 1799 1803 1804 1808 1812 1815 1817 1821 1822 1826 1830 1831 1835 1838 1840 1845 1846 1850 1854 1856 1859 1862 1865 1867 1871 1874 1876 1880 1883 1886 1889 1891 1894 1899 1901 1904 1906 1911 1912 1917 1920 1921 1926 1927 1932 1933 1936 1939 1942 1946 1948 1953 1956 1957 1962 1963 1968 1970 1973 1977 1978 1983 1986 1989 1992 1994 1998 2000 2004 2007 2010 2013 2015 2017 2021 2024 2027 2030 2034 2036 2040 2042 2044 2048 2051 2055 2057 2060 2063 2066 2070 2072 2074 2078 2082 2084 2087 2091 2093 2097 2100 2102 2106 2108 2111 2115 2118 2120 2123 2127 2129 2132 2136 2139 2142 2143 2147 2149 2154 2156 2158 2163 2166 2168 2172 2174 2177 2180 2183 2187 2189 2193 2195 2197 2201 2204 2207 2210 2212 2216 2219 2222 2226 2228 2232 2235 2238 2241 2242 2245 2249 2253 2256 2257 2262 2265 2267 2271 2274 2277 2278 2281 2284 2289 2292 2293 2297 2301 2303 2306 2308 2312 2314 2317 2320 2323 2326 2329 2332 2337 2338 2342 2344 2347 2351 2353 2357 2359 2362 2365 2368 2373 2375 2377 2380 2385 2387 2391 2394 2397 2400 2402 2404 2407 2410 2415 2416 2421 2422 2427 2429 2433 2434 2438 2440 2443 2448 2449 2452 2457 2459 2461 2465 2467 2471 2475 2476 2479 2484 2487 2488 2493 2494 2498 2501 2503 2506 2509 2512 2517 2519 2523 2524 2527 2531 2533 2537 2540 2544 2546 2549 2552 2556 2557 2562 2564 2568 2571 2573 2576 2578 2582 2585 2588 2591 2594 2596 2599 2603 2606 2608 2613 2614 2619 2622 2625 2628 2631 2634 2637 2640 2643 2645 2649 2650 2654 2657 2660 2664 2666 2669 2672 2675 2678 2681 2684 2686 2691 2692 2695 2698 2701 2705 2709 2712 2713 2716 2721 2723 2726 2730 2733 2736 2738 2742 2744 2748 2750 2753 2755 2759 2762 2765 2768 2772 2774 2778 2780 2784 2786 2789 2793 2795 2799 2802 2805 2808 2809 2813 2815 2820 2822 2824 2829 2831 2834 2836 2840 2843 2846 2849 2852 2854 2858 2861 2865 2868 2870 2872 2876 2879 2883 2885 2888 2891 2895 2897 2900 2903 2907 2909 2911 2915 2917 2921 2924 2928 2929 2934 2937 2940 2943 2945 2947 2951 2955 2958 2960 2964 2965 2968 2973 2976 2979 2982 2985 2987 2991 2994 2996 2999 3003 3004 3008 3011 3015 3017 3020 3023 3026 3029 3032 3035 3039 3041 3043 3046 3049 3052 3055 3058 3062 3064 3067 3071 3073 3077 3080 3083 3087 3089 3093 3096 3099 3101 3104 3106 3110 3113 3115 3118 3123 3125 3129 3131 3135 3138 3140 3143 3145 3149 3152 3155 3159 3160 3163 3166 3170 3172 3175 3178 3182 3186 3188 3191 3195 3197 3201 3203 3205 3209 3212 3215 3218 3221 3225 3226 3229 3233 3237 3240 3241 3245 3248 3252 3254 3257 3259 3263 3266 3270 3273 3274 3279 3281 3283 3288 3289 3294 3297 3300 3302 3306 3309 3310 3314 3318 3321 brock200_2
Graph with 200 nodes, 9 876 edges, and ω(G)= 12.Best-known
solution hassize 12.
Clique 1
27 48 55 70 105 120 121 135 145 149 158 183 brock200_4
Graph with 200 nodes, 13 089 edges, and ω(G)= 17.Best-known
solution hassize 17.
Clique 1
12 19 28 29 38 54 65 71 79 93 117 127 139 161 165 186 192 brock400_2
Graph with 400 nodes, 59 786 edges, and ω(G)= 29.Best-known
solution hassize 29.
Clique 1
18 20 39 68 73 85 90 92 93 108 134 135 142 150 178 186 207 221 234 252 260 262 276 304 311 348 365 380 388 brock400_4
Graph with 400 nodes, 59 765 edges, and ω(G)= 33.Best-known
solution hassize 33.
Clique 1
7 8 17 19 112 135 147 154 157 161 186 197 202 211 241 242 245 247 266 267 270 294 324 334 340 343 353 362 380 389 393 394 396 brock800_2
Graph with 800 nodes, 208 166 edges, and ω(G)= 24.Best-known
solution hassize 24.
Clique 1
13 56 85 110 131 156 161 215 259 272 324 349 384 415 418 446 461 497 505 581 650 695 696 793 brock800_4
Graph with 800 nodes, 207 643 edges, and ω(G)= 26.Best-known
solution hassize 26.
Clique 1
8 17 112 135 154 157 161 247 270 294 324 334 343 362 389 394 396 495 509 511 561 624 666 681 687 714 gen200_p0.9_44
Graph with 200 nodes, 17 910 edges, and ω(G)= 44.Best-known
solution hassize 44.
Clique 1
2 13 20 29 34 38 40 46 47 65 67 72 75 81 82 84 93 94 97 100 102 105 108 117 119 120 123 127 129 132 138 141 146 149 150 151 156 166 170 180 186 190 193 195 gen200_p0.9_55
Graph with 200 nodes, 17 910 edges, and ω(G)= 55.Best-known
solution hassize 55.
Clique 1
5 6 12 14 15 19 21 25 26 27 30 33 35 36 41 62 64 67 69 73 76 77 78 79 81 82 86 88 89 91 93 95 96 107 111 113 116 117 123 129 143 144 146 147 159 163 164 169 175 177 182 187 192 197 199 gen400_p0.9_55
Graph with 400 nodes, 71 820 edges, and ω(G)= 55.Best-known
solution hassize 55.
Clique 1
1 19 22 24 27 31 37 39 49 54 56 62 80 82 85 94 99 100 107 116 117 120 122 137 149 163 164 186 191 210 212 220 222 228 243 247 248 266 274 277 279 281 283 297 305 325 336 342 344 346 352 363 394 398 399 gen400_p0.9_65
Graph with 400 nodes, 71 820 edges, and ω(G)= 65.Best-known
solution hassize 65.
Clique 1
5 9 14 20 25 28 36 39 47 48 50 51 53 58 69 109 116 119 138 145 158 161 163 166 168 171 176 178 181 182 185 188 198 206 210 218 228 234 235 240 244 247 253 258 260 274 283 287 290 316 330 334 339 341 343 351 359 363 367 375 379 381 383 394 395 gen400_p0.9_75
Graph with 400 nodes, 71 820 edges, and ω(G)= 75.Best-known
solution hassize 75.
Clique 1
6 9 11 16 18 25 27 30 48 50 54 55 58 60 67 93 95 99 101 102 104 105 106 112 113 117 121 124 132 140 142 143 145 150 155 157 163 171 174 177 180 192 196 205 222 225 230 243 245 246 250 263 265 284 301 308 314 322 333 335 338 341 345 347 359 368 374 381 383 387 389 391 395 399 400 hamming10-4
Graph with 1 024 nodes, 434 176 edges, and ω(G)= 40.Best-known
solution hassize 40.
Clique 1
22 39 42 83 125 139 177 192 206 228 269 315 332 353 376 404 422 469 495 506 528 537 564 581 619 642 663 685 732 758 771 821 850 863 878 926 940 968 969 1011 hamming8-4
Graph with 256 nodes, 20 864 edges, and ω(G)= 16.Best-known
solution hassize 16.
Clique 1
11 18 37 64 78 87 100 121 136 157 170 179 193 220 239 246 keller4
Graph with 171 nodes, 9 435 edges, and ω(G)= 11.Best-known
solution hassize 11.
Clique 1
2 6 22 24 74 76 100 109 118 140 153 keller5
Graph with 776 nodes, 225 990 edges, and ω(G)= 27.Best-known
solution hassize 27.
Clique 1
6 11 30 34 49 75 84 93 111 117 166 240 261 324 361 427 433 457 462 471 499 539 545 572 581 595 612 keller6
Graph with 3 361 nodes, 4 619 898 edges, and ω(G)≥ 59.Best-known
solution hassize 59.
Clique 1
36 91 102 181 241 275 294 347 356 397 495 501 528 557 783 794 889 916 967 976 1088 1122 1385 1402 1408 1470 1509 1520 1548 1884 1889 1917 1971 1973 2005 2029 2083 2104 2235 2267 2325 2395 2473 2484 2594 2595 2638 2654 2727 2749 2752 2964 2973 3121 3179 3196 3256 3290 3309 p_hat300-1
Graph with 300 nodes, 10 933 edges, and ω(G)= 8.Best-known
solution hassize 8.
Clique 1
54 124 181 219 247 268 271 287 p_hat300-2
Graph with 300 nodes, 21 928 edges, and ω(G)= 25.Best-known
solution hassize 25.
Clique 1
4 26 38 40 48 49 56 75 76 139 149 159 165 174 190 199 205 231 237 255 259 273 274 281 296 p_hat300-3
Graph with 300 nodes, 33 390 edges, and ω(G)= 36.Best-known
solution hassize 36.
Clique 1
4 19 20 21 24 33 40 48 49 56 76 89 98 139 149 160 166 174 176 190 199 205 219 221 226 235 239 245 247 252 255 273 290 293 298 299 p_hat700-1
Graph with 700 nodes, 60 999 edges, and ω(G)= 11.Best-known
solution hassize 11.
Clique 1
117 151 306 334 397 459 513 528 537 559 686 p_hat700-2
Graph with 700 nodes, 121 728 edges, and ω(G)= 44.Best-known
solution hassize 44.
Clique 1
9 15 31 54 73 76 106 115 118 122 149 152 189 193 212 292 295 297 317 323 325 326 345 350 351 373 379 387 397 437 468 495 513 562 576 579 581 584 608 612 649 658 667 678 p_hat700-3
Graph with 700 nodes, 183 010 edges, and ω(G)62*.Best-known
solution hassize 62.
Clique 1
8 16 17 25 30 31 54 76 87 106 107 118 122 129 142 145 149 152 193 239 240 248 261 276 285 290 292 295 306 317 323 325 326 345 348 350 361 368 373 379 387 392 393 468 482 495 525 537 562 579 581 584 587 608 612 623 638 649 653 661 667 678 p_hat1500-1
Graph with 1 500 nodes, 284 923 edges, and ω(G)= 12.Best-known
solution hassize 12.
Clique 1
444 485 566 580 622 671 820 912 971 983 1139 1323 p_hat1500-2
Graph with 1 500 nodes, 568 960 edges, and ω(G)65*.Best-known
solution hassize 65.
Clique 1
26 68 72 131 139 173 214 261 274 277 290 309 358 392 396 403 423 428 434 438 440 444 450 514 561 562 564 615 622 689 691 738 749 767 819 826 838 863 878 906 917 920 960 974 990 1005 1039 1046 1056 1069 1072 1120 1145 1191 1209 1265 1330 1342 1385 1399 1411 1419 1478 1483 1485 p_hat1500-3
Graph with 1 500 nodes, 847 244 edges, and ω(G)94*.Best-known
solution hassize 94.
Clique 1
26 37 68 82 93 100 103 112 131 133 149 166 179 214 217 261 274 276 309 312 358 389 392 396 420 428 433 434 438 440 444 475 508 514 530 537 555 562 564 580 622 689 691 723 757 767 769 804 819 826 838 853 863 906 907 917 922 945 960 974 977 990 1002 1005 1020 1027 1034 1035 1046 1072 1120 1157 1167 1171 1244 1261 1265 1273 1339 1342 1385 1389 1394 1403 1411 1413 1416 1419 1460 1464 1471 1478 1485 1500