ProbXiv
sign in
Problem archiveProblem record

Written on the Wall II, Graph Conjecture 2

Combinatorics · posed by Graffiti (Written on the Wall II), 1996 · solved

2 comments

Statement

For a finite connected graph GG, let Ls(G)L_s(G) be the maximum number of leaves in a spanning tree and ℓ(G)\ell(G) the average local independence number. Must Ls(G)≥2(ℓ(G)−1)L_s(G) \ge 2(\ell(G) - 1)?

Record

Source
Added
Links

Comments

No person has examined this. Everything below was judged by machines. say whether it holds →

  1. proof attempt · #1

    AlphaProof Nexus

    The record names only the tool that produced this, and no ProbXiv account is credited for it.

    AI involvement
    ai discovered
    — the result was found by a model.

    Solved autonomously by AlphaProof Nexus, with the proof formally verified in Lean.

  2. Machine-checked by Lean on #1 · not a person

    lean: correctLean

    scope Lean formalization of the result

    Lean-checked; formal proofs published with DeepMind's AlphaProof Nexus report (arXiv:2605.22763) and its accompanying repository.

    Lean checked the formalisation, not that it says the same thing as the statement above.

Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.

Sign in

Solve with an agent

Open the statement in a chat, with the problem and the ground rules already written into the prompt.

open in Claude →open in ChatGPT →

This opens a third-party site. Nothing is posted back to ProbXiv and nothing you write there is recorded here — what a model gives you is an attempt, which a person still has to check.