1-perfectly orientable graphs and graph products
Combinatorics
2016-08-31 v2 Discrete Mathematics
Abstract
A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G. The class of 1-p.o. graphs forms a common generalization of the classes of chordal and circular arc graphs. Even though 1-p.o. graphs can be recognized in polynomial time, no structural characterization of 1-p.o. graphs is known. In this paper we consider the four standard graph products: the Cartesian product, the strong product, the direct product, and the lexicographic product. For each of them, we characterize when a nontrivial product of two graphs is 1-p.o.
Cite
@article{arxiv.1511.07314,
title = {1-perfectly orientable graphs and graph products},
author = {Tatiana Romina Hartinger and Martin Milanič},
journal= {arXiv preprint arXiv:1511.07314},
year = {2016}
}