Role colouring graphs in hereditary classes

Christopher Purcell; Puck Rombach

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arXiv · 1802.10180

Role colouring graphs in hereditary classes

Christopher Purcell·Puck Rombach

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Abstract

We study the computational complexity of computing role colourings of graphs in hereditary classes. We are interested in describing the family of hereditary classes on which a role colouring with k colours can be computed in polynomial time. In particular, we wish to describe the boundary between the "hard" and "easy" classes. The notion of a boundary class has been introduced by Alekseev in order to study such boundaries. Our main results are a boundary class for the k-role colouring problem and the related k-coupon colouring problem which has recently received a lot of attention in the literature. The latter result makes use of a technique for generating regular graphs of arbitrary girth which may be of independent interest.

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Christopher Purcell, Puck Rombach. 2018-02-27. Role colouring graphs in hereditary classes. https://arxiv.org/abs/1802.10180

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