Add 10 WOWII open conjectures (batch 2)#3796
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henrykmichalewski wants to merge 1 commit intogoogle-deepmind:mainfrom
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Add 10 WOWII open conjectures (batch 2)#3796henrykmichalewski wants to merge 1 commit intogoogle-deepmind:mainfrom
henrykmichalewski wants to merge 1 commit intogoogle-deepmind:mainfrom
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Medium-difficulty conjectures using distEven(v), tree(G), and related invariants. ## Conjectures - 23, 24, 63: involve distEven (min vertices at even distance) - 72, 84, 85: involve tree(G) (largest induced tree) - 91, 96: upper bounds on b(G) / α(G) - 189: Hamiltonian via max distEven + σ(G) (2-domination) - 199: Hamiltonian via tree(G) and vertex connectivity κ(G) ## New definitions (local, self-contained) - distEven G v - largestInducedTreeSize (reused from batch 1) - twoDominationNumber (new, for σ(G)) - vertexConnectivity (new, for κ(G)) ## Tests Each file has 1-2 fully-proved @[category test] examples. Reference: E. DeLaVina, Written on the Wall II http://cms.dt.uh.edu/faculty/delavinae/research/wowII/ Assisted by Claude (Anthropic).
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This branch accumulates all WOWII batches beyond batch 1 (google-deepmind#3795) and batch 2 (google-deepmind#3796). Total new files: 48, covering ~50 new invariants. Batches: - 3 (5 files): residue, distMin/Max — 18, 59, 61, 65, 109 - 4 (9 files): path/tree hard cases, C₄ — 31, 36, 100, 103, 133, 142, 143, 144, 314 - 5 (5 files): alphaCore, graphSquare, triangles — 101, 145, 146, 160, 291 - 6 (5 files): matching, circumference, oddGirth, etc. - 7 (8 files): length, toughness, distOdd, edgeConnectivity, mode, power, freqMaxL, residue2 - 8 (8 files): arboricity, degeneracy, metricDimension, geodeticNumber, modeMax, medianDegree, evenModeMin, girthComplement - 9 (8 files): achromaticNumber, bandwidth, boxicity, crossingNumber, isoperimetric, rainbowConnection, romanDomination, thickness Many have proved theorems (particularly classical results stated with sorry). Each file includes sanity-check tests. This is a staging branch for easier review / cherry-picking into smaller PRs. Assisted by Claude (Anthropic).
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Adds 10 open conjectures from WOWII (Written on the Wall II) by E. DeLaViña.
Follow-up to #3795 (batch 1, 16 conjectures).
Reference: http://cms.dt.uh.edu/faculty/delavinae/research/wowII/
Conjectures
New definitions (local to each file, self-contained)
distEven G v— count of vertices at even distance from vlargestInducedTreeSize— reused from batch 1twoDominationNumber— σ(G), 2-domination numbervertexConnectivity— κ(G), for Conj 199Each file is self-contained (definitions copied as needed) to keep PRs atomic.
Tests
All 10 files include 1-2 fully-proved
@[category test]examples.Build
Passes cleanly.
Assisted by Claude (Anthropic).