Erdős problem 944 · problems.science

Let $k \ge 4$ and $r\ge 1$ . Must there exist a graph $G$ with chromatic number $k$ such that every vertex is critical, yet every critical set of edges has size $>r$ ?

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FormalConjectures/ErdosProblems/

944.lean

Retained formal statement2 of 7

Let $k \ge 4$ . Must there exist a graph $G$ with chromatic number $k$ such that every vertex is critical, yet every critical set of edges has size $>1$ ?

This was conjectured by Dirac in 1970.

FormalConjectures/ErdosProblems/944.leanErdos944.erdos_944.variants.dirac_conjecture1 lineExact file

1True ↔ ∀ k ≥ 4, ∃ V G, Erdos944.SimpleGraph.IsErdos944 G k 1

OpenStatement only, no proof

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