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arXiv · 2003.05606

Orientations without forbidden patterns on three vertices

Santiago Guzmán-Pro·César Hernández-Cruz
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Abstract

Given a set $F$ of oriented graphs, a graph $G$ is an $F$-graph if it admits an $F$-free orientation. Building on previous work by Bang-Jensen and Urrutia, we propose a master algorithm that determines if a graph admits an $F$-free orientation when $F$ is a subset of the orientations of $P_3$ and the transitive triangle. We extend previous results of Skrien by studying the class of $F$-graphs, when $F$ is any set of oriented graphs of order three. Structural characterizations for all such sets are provided, except for the so-called perfectly-orientable graphs and one of its subclasses, which remain as open problems.

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Santiago Guzmán-Pro, César Hernández-Cruz. 2023-01-13. Orientations without forbidden patterns on three vertices. https://arxiv.org/abs/2003.05606

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