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OP-6989OpenCombinatorics

Winner complexity of Node Kayles on subcubic trees

TheoremDB P2930 · combinatorial games

Inferred from the community field; finer classification has not been reviewed.

Source catalogue assessmentAs of 2026-09-08Source & evidence ↓

Problem statement

Given a finite tree TT of maximum degree at most three as a Node Kayles position, what is the complexity of deciding whether the next player has a winning strategy? In particular, is the problem polynomial-time solvable or PSPACE-complete?

Lean 4

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Background

Additional formulation recorded by the source

Classify the language {T:T is a finite tree, Δ(T)≤3, and the next Node Kayles player wins on T}\{T:T\text{ is a finite tree},\ \Delta(T)\le3,\text{ and the next Node Kayles player wins on }T\}.

Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

Open. No signed Lean verification is attached to this problem or its selected resolution.

References
  1. [1]TheoremDB P2930 link

Recorded progress

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Discussion

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