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arXiv · 2103.07886

Decomposing and colouring some locally semicomplete digraphs

Pierre Aboulker·Guillaume Aubian·Pierre Charbit
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Abstract

A digraph is semicomplete if any two vertices are connected by at least one arc and is locally semicomplete if the out-neighbourhood and the in-neighbourhood of any vertex induce a semicomplete digraph. In this paper we study various subclasses of locally semicomplete digraphs for which we give structural decomposition theorems. As a consequence we obtain several applications, among which an answer to a conjecture of Naserasr and the first and third authors: if an oriented graph is such that the out-neighbourhood of every vertex induces a transitive tournament, then one can partition its vertex set into two acyclic digraphs.

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Pierre Aboulker, Guillaume Aubian, Pierre Charbit. 2021-03-14. Decomposing and colouring some locally semicomplete digraphs. https://arxiv.org/abs/2103.07886

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