A semidefinite programming-based heuristic for graph coloring

Authors:
Igor Dukanovic;Franz Rendl
Affiliations:
EPF, University of Maribor, Razlagova 14, 2000 Maribor, Slovenia;Institut für Mathematik, Universität Klagenfurt, 9020 Klagenfurt, Austria
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

The Lovasz @q-function is a well-known polynomial lower bound on the chromatic number. Any near-optimal solution of its semidefinite programming formulation carries valuable information on how to color the graph. A self-contained presentation of the role of this formulation in obtaining heuristics for the graph coloring problem is presented. These heuristics could be useful for coloring medium sized graphs as numerical results on DIMACS benchmark graphs indicate.