English

Contractions in perfect graph

Combinatorics 2024-01-24 v1 Discrete Mathematics

Abstract

In this paper, we characterize the class of {\em contraction perfect} graphs which are the graphs that remain perfect after the contraction of any edge set. We prove that a graph is contraction perfect if and only if it is perfect and the contraction of any single edge preserves its perfection. This yields a characterization of contraction perfect graphs in terms of forbidden induced subgraphs, and a polynomial algorithm to recognize them. We also define the utter graph u(G)u(G) which is the graph whose stable sets are in bijection with the co-2-plexes of GG, and prove that u(G)u(G) is perfect if and only if GG is contraction perfect.

Keywords

Cite

@article{arxiv.2401.12793,
  title  = {Contractions in perfect graph},
  author = {Alexandre Dupont-Bouillard and Pierre Fouilhoux and Roland Grappe and Mathieu Lacroix},
  journal= {arXiv preprint arXiv:2401.12793},
  year   = {2024}
}

Comments

11 pages, 4 figures

R2 v1 2026-06-28T14:24:45.934Z