Recognition of Graphs with Convex Quadratic Stability Number
Maria F. Pacheco, Domingos M. Cardoso, Theodore E. Simos, George Psihoyios, Ch. Tsitouras · AIP conference proceedings · 2009
A stable set of a graph is a set of mutually non‐adjacent vertices. The determination of a maximum size stable set, which is called maximum stable set, and the determination of its size, which is called stability number, are central combinatorial optimization problems. However, given a nonnegative integer k, to determine if a graph G has a stable set of size k is NP‐complete. In this paper we deal with graphs for which the stability number can be determined by solving a convex quadratic programming problem. Such graphs were introduced in [13] and are called graphs with convex‐QP stability number. A few algorithmic techniques for the recognition of this type of graphs in particular families are presented.