A fast algorithm for coloring Meyniel graphs

https://doi.org/10.1016/0095-8956(90)90078-EGet rights and content
Under an Elsevier user license
open archive

Abstract

We color the nodes of a graph by first applying successive contractions to non-adjacent nodes until we get a clique; then we color the clique and decontract the graph. We show that this algorithm provides a minimum coloring and a maximum clique for any Meyniel graph by using a simple rule for choosing which nodes are to be contracted. This O(n3) algorithm is much simpler than those already existing for Meyniel graphs. Moreover, the optimality of this algorithm for Meyniel graphs provides an alternate nice proof of the following result of Hoàng: a graph G is Meyniel if and only if, for any induced subgraph of G, each node belongs to a stable set that meets all maximal cliques. Finally we give a new characterization for Meyniel graphs.

Cited by (0)