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 statement5 of 7

Erdős, Gyárfás and Ruszinkó [EGR98]: $h_5(G) \leq \frac{n-1}{2}$ for every connected triangle-free graph $G$ on $n$ vertices.

FormalConjectures/ErdosProblems/619.leanErdos619.erdos_619.variants.h_five_le2 linesExact file

1∀ {V : Type u_1} [inst : Fintype V] (G : SimpleGraph V),2  G.Connected → G.CliqueFree 3 → ↑(Erdos619.minNewEdges 5 G) ≤ (↑(Fintype.card V) - 1) / 2

SolvedStatement only, no proof

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