Erdős problem 619 · problems.science

Erdős Problem 619 [EGR98, Er99]: For a triangle-free graph $G$ let $h_r(G)$ be the smallest number of edges that need to be added to $G$ so that it has diameter $r$ (while preserving the property of being triangle-free). Is it true that there exists a constant $c>0$ such that if $G$ is a connected graph on $n$ vertices then $h_4(G)<(1-c)n$ ?

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FormalConjectures/ErdosProblems/

619.lean

Retained formal statement2 of 7

A triangle-free graph that already has diameter at most r needs no new edges.

FormalConjectures/ErdosProblems/619.leanErdos619.erdos_619.test.minNewEdges_eq_zero1 lineExact file

1∀ {V : Type u_1} {r : ℕ} {G : SimpleGraph V}, G.CliqueFree 3 → G.ediam ≤ ↑r → Erdos619.minNewEdges r G = 0

TestStatement only, no proof

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