- On forests, stable sets and polyhedras associated with clique partitions Denis Cornaz (cornazmath.jussieu.fr) Abstract: Let $G=(V,E)$ be a simple graph on $n$ nodes. We show how to construct a partial subgraph $D$ of the line graph of $G$ satisfying the identity: $\overline \chi(G)+\alpha(D)=n$, where $\overline \chi(G)$ denotes the minimum number of cliques in a clique partition of $G$ and $\alpha(D)$ denotes the maximum size of a stable set of $D$. This is based on correspondences between the cliques partitions and the clique-connecting forests of $G$. We use this to develop a cutting-plane algorithm for the graph coloring problem that is tested on random and DIMACS benchmark graphs. Keywords: Graph coloring, maximum stable set, polytope. Category 1: Combinatorial Optimization Category 2: Combinatorial Optimization (Graphs and Matroids ) Category 3: Combinatorial Optimization (Polyhedra ) Citation: Download: [Postscript]Entry Submitted: 03/14/2006Entry Accepted: 03/14/2006Entry Last Modified: 03/14/2006Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.