A one-to-one correspondence between colorings and stable sets

Authors:
Denis Cornaz;Vincent Jost
Affiliations:
LIMOS, Complexe scientifique des Cézeaux, 63177 Aubière cedex, France;ROSO - TRANSP-OR, EPFL - Lausanne, Switzerland
Venue:
Operations Research Letters
Year:
2008

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Abstract

Given a graph G, we construct an auxiliary graph G@? with m@? vertices such that the set of all stable sets of G@? is in one-to-one correspondence with the set of all colorings of G. Then, we show that the Max-Coloring problem in G reduces to the Maximum Weighted Stable set problem in G@?.