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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619.lean

Retained formal statement4 of 7

Erdős, Gyárfás and Ruszinkó [EGR98]: every connected triangle-free graph on a finite vertex set can be extended, by adding edges, to a triangle-free graph of diameter at most $3$ . This shows that the infimum defining minNewEdges r G ranges over a nonempty set for every 3 ≤ r.

FormalConjectures/ErdosProblems/619.leanErdos619.erdos_619.variants.add_edges_diam_three2 linesExact file

1∀ {V : Type u_1} [Fintype V] (G : SimpleGraph V),2  G.Connected → G.CliqueFree 3 → ∃ H, G ≤ H ∧ H.CliqueFree 3 ∧ H.ediam ≤ 3

SolvedStatement only, no proof

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