Decomposing and colouring some locally semicomplete digraphs
Combinatorics
2022-12-07 v3 Discrete Mathematics
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.
Cite
@article{arxiv.2103.07886,
title = {Decomposing and colouring some locally semicomplete digraphs},
author = {Pierre Aboulker and Guillaume Aubian and Pierre Charbit},
journal= {arXiv preprint arXiv:2103.07886},
year = {2022}
}
Comments
Nothing new in this version, which only corrected wrongly typed author names