Stable sets and polynomials. (English) Zbl 0792.05082

The author surveys various applications of methods involving nonlinear commutative algebra to the stable set problem for graphs. In particular, he discusses a procedure for generating the facets of the stable set polytope. If a class of graphs \(G\) is such that all the facets of the stable set polytopes can be generated this way in a bounded number of steps, then the stability numbers of these graphs \(G\) are computable in polynomial time. Perfect, \(t\)-perfect, and \(h\)-perfect graphs have this property.


05C35 Extremal problems in graph theory
05C15 Coloring of graphs and hypergraphs
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