English

Role colouring graphs in hereditary classes

Computational Complexity 2018-03-01 v1 Combinatorics

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.

Keywords

Cite

@article{arxiv.1802.10180,
  title  = {Role colouring graphs in hereditary classes},
  author = {Christopher Purcell and Puck Rombach},
  journal= {arXiv preprint arXiv:1802.10180},
  year   = {2018}
}
R2 v1 2026-06-23T00:35:59.116Z