On the complexity of colouring antiprismatic graphs
Abstract
A graph G is prismatic if for every triangle T of G, every vertex of G not in T has a unique neighbour in T. The complement of a prismatic graph is called \emph{antiprismatic}. The complexity of colouring antiprismatic graphs is still unknown. Equivalently, the complexity of the clique cover problem in prismatic graphs is not known. Chudnovsky and Seymour gave a full structural description of prismatic graphs. They showed that the class can be divided into two subclasses: the orientable prismatic graphs, and the non-orientable prismatic graphs. We give a polynomial time algorithm that solves the clique cover problem in every non-orientable prismatic graph. It relies on the the structural description and on later work of Javadi and Hajebi. We give a polynomial time algorithm which solves the vertex-disjoint triangles problem for every prismatic graph. It does not rely on the structural description.
Keywords
Cite
@article{arxiv.1910.11001,
title = {On the complexity of colouring antiprismatic graphs},
author = {Myriam Preissmann and Cléophée Robin and Nicolas Trotignon},
journal= {arXiv preprint arXiv:1910.11001},
year = {2023}
}