Add 16 WOWII open conjectures (batch 1)#3795
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henrykmichalewski wants to merge 1 commit intogoogle-deepmind:mainfrom
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Add 16 WOWII open conjectures (batch 1)#3795henrykmichalewski wants to merge 1 commit intogoogle-deepmind:mainfrom
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…h 1) Adds 16 open WOWII conjectures following the existing pattern in FormalConjectures/WrittenOnTheWallII/. Each file includes 1-2 fully-proved sanity-check examples testing the invariants used. ## Conjectures added ### Spanning tree leaves Ls (1) - Conjecture 3: Ls(G) ≥ γ_i(G) · max temp(v) ### Largest induced bipartite subgraph b(G) (5) - Conjecture 13: b(G) ≥ diam(G) + max l(v) - 1 - Conjecture 16: b(G) ≥ 2(rad(G)-1) + max l(v) - Conjecture 17: b(G) ≥ α(G) + ⌈diam(G)/3⌉ - Conjecture 20: b(G) ≥ n / ⌊deg_avg⌋ - Conjecture 22: b(G) ≥ ⌊α(G) + distavg(M)⌋ ### Longest induced path (2) - Conjecture 32: path(G) ≥ ⌈2·distavg(M,V)⌉ - Conjecture 33: path(G) ≥ ⌈distavg(C,V) + distavg(M,V)⌉ ### Induced tree (2) - Conjecture 141: tree(G) ≥ (girth-2)/2 + max l(v) - Conjecture 200: tree(G) = ⌈1 + λ_avg⌉ implies Hamiltonian path ### Hamiltonian path sufficient conditions (2) - Conjecture 194: α(G) ≤ 1 + λ_avg implies Hamiltonian path - Conjecture 198a: b(G) ≤ 2 + ecc_avg implies Hamiltonian path ### Well totally dominated (4) - Conjecture 315: α(G) = |pendants| implies well totally dominated - Conjecture 316: |pendants| ≥ deg_avg implies well totally dominated - Conjecture 322: n ≥ 5, max l(v) ≤ 1 implies well totally dominated - Conjecture 327: 3γ(G) = γ_i(G) implies well totally dominated ## New definitions added locally - largestInducedTreeSize (used in 141, 200) - averageEccentricity (used in 198a) - pendantVertices (used in 315, 316) - IsTotalDominatingSet, IsMinimalTotalDominatingSet, isWellTotallyDominated (shared across 315/316/322/327) Reference: E. DeLaVina, Written on the Wall II, Conjectures of Graffiti.pc 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 16 open conjectures from the WOWII (Written on the Wall II) database by E. DeLaViña, following the existing pattern in FormalConjectures/WrittenOnTheWallII/.
Reference: http://cms.dt.uh.edu/faculty/delavinae/research/wowII/
Scope
@[category research open, AMS 5])New definitions
largestInducedTreeSize(local, used in 141 and 200)averageEccentricity(local, used in 198a)pendantVertices(shared across 315, 316)IsTotalDominatingSet,IsMinimalTotalDominatingSet,isWellTotallyDominated(shared across 315/316/322/327, defined in 315 and imported)Batch strategy
This is batch 1 of ~4 batches covering 40 open WOWII conjectures. This batch targets the easiest formalizations (existing or trivial-to-add invariants). Subsequent batches will add residue, distmin/distmax, σ (2-domination), etc.
Checks
Assisted by Claude (Anthropic).