A Size Condition for Diameter Two Orientable Graphs

Garner Cochran; Éva Czabarka; Peter Dankelmann; László Székely

A Size Condition for Diameter Two Orientable Graphs

Combinatorics 2018-08-29 v1

Authors: Garner Cochran , Éva Czabarka , Peter Dankelmann , László Székely

Abstract

It was conjectured by Koh and Tay [Graphs Combin. 18(4) (2002), 745--756] that for $n\geq 5$ every simple graph of order $n$ and size at least $\binom{n}{2}-n+5$ has an orientation of diameter two. We prove this conjecture and hence determine for every $n\geq 5$ the minimum value of $m$ such that every graph of order $n$ and size $m$ has an orientation of diameter two.

Keywords

graph theory

Cite

@article{arxiv.1808.08996,
  title  = {A Size Condition for Diameter Two Orientable Graphs},
  author = {Garner Cochran and Éva Czabarka and Peter Dankelmann and László Székely},
  journal= {arXiv preprint arXiv:1808.08996},
  year   = {2018}
}

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