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 which is the graph whose stable sets are in bijection with the co-2-plexes of , and prove that is perfect if and only if is contraction perfect.
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