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Strengthening the Lovász $$\theta(\overline G)$$ bound for graph coloring. (English) Zbl 1059.05052
Summary: The Lovász $$\theta$$-number is a way to approximate the independence number of a graph, but also its chromatic number. We express the Lovász bound as the continuous relaxation of a discrete Lovász $$\theta$$-number which we derive from D. Karger et al.’s formulation [J. ACM 45, 246–265 (1998; Zbl 0904.68116)], and which is equal to the chromatic number. We also give another relaxation à la Schrijver-McEliece, which is better than the Lovász $$\theta$$-number.

##### MSC:
 05C15 Coloring of graphs and hypergraphs 05C35 Extremal problems in graph theory 90C27 Combinatorial optimization
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