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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7 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

619.lean

Retained formal statement3 of 7

The graph with a single vertex is triangle-free and has diameter 0, so it needs no new edges to reach diameter at most 4.

FormalConjectures/ErdosProblems/619.leanErdos619.erdos_619.test.minNewEdges_singleton1 lineExact file

1Erdos619.minNewEdges 4 ⊥ = 0

TestStatement only, no proof

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