This web page contains a table of the independence numbers of Paley graphs for graphs of size less than 7000. The first column is the size of the Paley graph, the second column is the independence number and the third column is the time in seconds my program required to compute the independence number. For some definitions and related material see my paper Lower Bounds for Small Diagonal Ramsey Numbers .
P I(G(P)) Compute time
13 3 0.000007
17 3 0.000007
29 4 0.000009
37 4 0.000011
41 5 0.000011
53 5 0.000015
61 5 0.000019
73 5 0.000025
89 5 0.000037
97 6 0.000038
101 5 0.000033
109 6 0.000065
113 7 0.000050
137 7 0.000120
149 7 0.000103
157 7 0.000147
173 8 0.000185
181 7 0.000224
193 7 0.000290
197 8 0.000143
229 9 0.000347
233 7 0.000602
241 7 0.000732
257 7 0.000864
269 8 0.000484
277 8 0.000887
281 7 0.000752
293 8 0.000978
313 8 0.001793
317 9 0.001500
337 9 0.001334
349 9 0.000749
353 9 0.002125
373 8 0.002208
389 9 0.001775
397 9 0.002170
401 9 0.002111
409 9 0.002106
421 9 0.004104
433 11 0.002067
449 9 0.003862
457 11 0.002235
461 11 0.003928
509 9 0.005487
521 9 0.009585
541 11 0.004708
557 11 0.009513
569 9 0.016556
577 10 0.005372
593 11 0.004671
601 11 0.005425
613 12 0.009734
617 11 0.006137
641 11 0.020892
653 11 0.008248
661 11 0.022175
673 11 0.019888
677 11 0.019734
701 10 0.015739
709 10 0.034223
733 11 0.051571
757 11 0.026281
761 11 0.013380
769 11 0.057141
773 11 0.030352
797 9 0.084038
809 11 0.045653
821 12 0.039114
829 11 0.034601
853 13 0.022427
857 13 0.055505
877 13 0.053422
881 11 0.047707
929 13 0.048097
937 11 0.081391
941 11 0.086923
953 11 0.074663
977 13 0.088209
997 13 0.057973
1009 11 0.150143
1013 11 0.186595
1021 11 0.208893
1033 11 0.214028
1049 11 0.183206
1061 12 0.160141
1069 12 0.086815
1093 12 0.228292
1097 12 0.135008
1109 11 0.375034
1117 12 0.270319
1129 13 0.177004
1153 13 0.355548
1181 12 0.364227
1193 11 0.229219
1201 13 0.153348
1213 13 0.385951
1217 13 0.385859
1229 12 0.368887
1237 13 0.119625
1249 13 0.184837
1277 11 0.985318
1289 15 0.276777
1297 13 0.445316
1301 13 0.210889
1321 13 0.264771
1361 12 0.984924
1373 14 0.593265
1381 12 0.963412
1409 13 0.459101
1429 13 0.523972
1433 13 1.142867
1453 12 0.725411
1481 15 0.501307
1489 13 1.476071
1493 12 0.933219
1549 13 1.717272
1553 13 1.354756
1597 13 1.353653
1601 13 1.478373
1609 13 1.169198
1613 14 0.438527
1621 13 2.505310
1637 13 2.124091
1657 13 2.402308
1669 13 2.090278
1693 14 1.945108
1697 13 1.298699
1709 13 1.541647
1721 13 2.387255
1733 13 1.720724
1741 17 0.686220
1753 13 1.743254
1777 15 0.763413
1789 13 1.168310
1801 14 1.340100
1861 13 5.474797
1873 13 4.516053
1877 15 2.941568
1889 15 0.666935
1901 14 3.832357
1913 15 2.856852
1933 13 4.554835
1949 14 1.699544
1973 13 3.637919
1993 13 4.595217
1997 14 2.540470
2017 13 7.596363
2029 14 2.171696
2053 13 3.744369
2069 14 3.979653
2081 14 3.200946
2089 14 3.434666
2113 13 5.017495
2129 13 4.638498
2137 13 7.053780
2141 13 8.996544
2153 13 5.862014
2161 17 3.253700
2213 15 3.093256
2221 15 2.848334
2237 13 8.739523
2269 14 9.434536
2273 15 3.558563
2281 17 1.287725
2293 15 2.738433
2297 15 8.065717
2309 15 6.551955
2333 14 6.335688
2341 13 16.091866
2357 15 11.946546
2377 13 14.079785
2381 13 25.010178
2389 16 4.865674
2393 14 18.669997
2417 15 12.416451
2437 15 10.890214
2441 14 15.866624
2473 14 19.938588
2477 15 14.280774
2521 15 14.174413
2549 15 6.334592
2557 15 10.532561
2593 13 38.559454
2609 15 24.960383
2617 15 30.454765
2621 16 5.649500
2633 15 20.874122
2657 15 24.426053
2677 15 13.954597
2689 17 14.446509
2693 16 9.644279
2713 15 28.441826
2729 19 2.618208
2741 13 38.519333
2749 15 12.836313
2753 15 11.210253
2777 15 38.143524
2789 15 22.066494
2797 15 30.775191
2801 14 47.120004
2833 15 14.991742
2837 15 15.880804
2857 15 43.360516
2861 16 22.271826
2897 15 14.088529
2909 15 58.160507
2917 15 39.513078
2953 15 25.042091
2957 15 22.312524
2969 17 14.299944
3001 17 43.112469
3037 16 42.156233
3041 15 91.165062
3049 16 54.985819
3061 15 89.569896
3089 15 73.562767
3109 15 77.951441
3121 15 71.437270
3137 17 18.893293
3169 19 15.208318
3181 16 77.447867
3209 15 47.123829
3217 17 42.959340
3221 16 29.315167
3229 15 110.638680
3253 16 61.397669
3257 15 96.693266
3301 17 67.422031
3313 17 32.157069
3329 15 60.862807
3361 17 17.301038
3373 15 47.560711
3389 15 102.601171
3413 15 65.349836
3433 17 32.566060
3449 15 59.725850
3457 17 80.374357
3461 16 117.611192
3469 17 60.255806
3517 17 36.465540
3529 19 18.291067
3533 16 90.225348
3541 15 133.701601
3557 17 81.583647
3581 17 46.768318
3593 16 127.906172
3613 15 193.974084
3617 17 82.179805
3637 16 177.227322
3673 19 47.330734
3677 15 125.006894
3697 15 214.241735
3701 17 54.188442
3709 16 196.507414
3733 17 59.141275
3761 17 80.127531
3769 17 86.886251
3793 17 174.679481
3797 17 49.898096
3821 17 234.925174
3833 19 91.573525
3853 15 309.739387
3877 16 88.356253
3881 17 236.937520
3889 17 86.418935
3917 17 208.995221
3929 19 94.322855
3989 16 321.176847
4001 17 158.129269
4013 15 221.335041
4021 16 350.624034
4049 17 123.475066
4057 17 95.676238
4073 17 82.513800
4093 15 531.699791
4129 17 212.068500
4133 16 436.828083
4153 17 140.551218
4157 17 305.599743
4177 17 118.311222
4201 17 324.029508
4217 15 332.032256
4229 17 225.792990
4241 17 166.980902
4253 16 230.540834
4261 17 367.650757
4273 17 245.352831
4289 17 429.944562
4297 17 551.510878
4337 17 160.760985
4349 17 167.164567
4357 17 125.499862
4373 17 388.400173
4397 17 290.753925
4409 17 491.425883
4421 17 508.484897
4441 15 652.696527
4457 15 622.196858
4481 17 525.356566
4493 19 407.034832
4513 17 393.121655
4517 17 660.825287
4549 17 670.463904
4561 17 651.830974
4597 17 371.946932
4621 17 770.248782
4637 17 971.181135
4649 17 454.350578
4657 17 375.762366
4673 17 690.943064
4721 17 324.084560
4729 17 285.336186
4733 17 460.404880
4789 17 1123.879110
4793 16 561.733008
4801 19 454.407240
4813 17 486.628880
4817 17 985.273473
4861 18 303.699549
4877 17 399.737197
4889 19 455.799284
4909 17 387.931275
4933 17 779.367855
4937 17 995.304878
4957 17 582.158323
4969 17 450.793464
4973 17 635.263253
4993 17 649.512720
5009 18 452.040643
5021 16 1699.930703
5077 19 1039.649479
5081 17 1728.411815
5101 17 1334.500731
5113 19 289.765951
5153 17 510.318298
5189 17 638.578261
5197 16 1978.801436
5209 19 315.253774
5233 17 1330.902767
5237 18 950.256062
5261 17 1464.873822
5273 21 691.491310
5281 17 1389.458136
5297 17 1171.860088
5309 17 2187.538571
5333 17 999.891795
5381 18 1732.441370
5393 17 2361.278046
5413 18 869.170992
5417 19 725.675949
5437 17 972.540526
5441 17 2152.385514
5449 17 1363.437785
5477 17 980.855529
5501 16 1834.078119
5521 19 476.460763
5557 17 1904.292306
5569 18 1161.662621
5573 19 1340.567765
5581 17 1038.393086
5641 19 1912.572846
5653 17 3956.425758
5657 18 1253.345864
5669 17 3448.368779
5689 19 1499.865191
5693 17 3736.500569
5701 17 3834.152908
5717 17 2954.532677
5737 17 1432.181630
5741 18 909.483291
5749 18 1406.002342
5801 17 3641.505481
5813 17 4298.503993
5821 17 4102.030167
5849 17 4197.883107
5857 17 4728.425267
5861 17 1795.845985
5869 17 4677.236205
5881 19 887.553960
5897 17 3518.535617
5953 17 2066.597348
5981 17 4822.357179
6029 18 4140.311782
6037 19 1820.431672
6053 17 2030.064196
6073 19 2740.631401
6089 17 2542.541001
6101 18 2200.690523
6113 19 2541.136080
6121 18 2781.605084
6133 18 4476.917290
6173 17 7505.557813
6197 17 4852.137364
6217 19 1168.800517
6221 17 2983.757576
6229 19 3933.857243
6257 19 2762.010228
6269 17 3426.205518
6277 17 7471.050558
6301 19 2593.935525
6317 19 2873.981866
6329 19 2703.417342
6337 17 9862.973450
6353 17 4381.020172
6361 18 6235.792381
6373 17 6550.961531
6389 19 4070.616821
6397 18 7084.050552
6421 17 4765.196983
6449 19 1604.462722
6469 17 5609.277048
6473 19 4910.024754
6481 17 4897.979267
6521 21 2888.354216
6529 17 4553.512724
6553 19 5388.416230
6569 19 1882.608740
6577 19 3270.935085
6581 17 11063.210265
6637 18 5140.718001
6653 19 2574.798856
6661 19 7750.966270
6673 19 2334.400835
6689 19 2251.387632
6701 17 13085.247154
6709 17 6467.994968
6733 18 7214.095653
6737 18 9874.193841
6761 20 3868.291140
6781 19 2325.315091
6793 19 3681.520311
6829 18 13813.111353
6833 19 7129.099826
6841 17 13641.084521
6857 17 17407.028989
6869 19 2891.963385
6917 18 8068.283225
6949 18 11558.841513
6961 19 7667.036558
6977 18 6666.677116
6997 17 10683.233208
[
IBM Research home page |
James B. Shearer's home page |
Up
]
[
IBM home page |
Order |
Search |
Contact IBM |
Legal
]