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Article Dans Une Revue Algorithmica Année : 2020

On the complexity of colouring antiprismatic graphs

Résumé

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.

Dates et versions

hal-02392476 , version 1 (04-12-2019)

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Myriam Preissmann, Cléophée Robin, Nicolas Trotignon. On the complexity of colouring antiprismatic graphs. Algorithmica, 2020, 83 (2), pp.589-612. ⟨10.1007/s00453-020-00767-7⟩. ⟨hal-02392476⟩
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