Erdős problem 944

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 $>r$ ?

Sources

The source's own material, retained exactly.

7 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

944.lean

Retained formal statement4 of 7

The case $k=4$ and $r=1$ remains open: Are there $4$ -critical graphs without any critical edges?

FormalConjectures/ErdosProblems/944.leanErdos944.erdos_944.variants.dirac_conjecture.k_eq_four1 lineExact file

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

OpenStatement only, no proof