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IASI Research Report n. 209 (Previous Next) Paola Bertolazzi,

Sassano A.A decomposition strategy for the vertex cover problem.ABSTRACT Given a graph G(V, E), where V = {v_1, ..., v_n} is the set of nodes and E = {e_ij = {v_i, v_j}} is the set of edges, a vertex cover in G is a subset .... with the property that every edge ....... is incident to some node of C. If a weight ...... is associated to each node vi E V then the weight w(C) of a vertex cover ...... is given by w(C) = .... The minimum weight vertex cover problem (WVC) is the problem of finding the vertex cover having minimum weight.
This paper presents a decomposition strategy for solving the minimum weight vertex cover problem for general graphs. Moreover it introduces a new class of graphs having the property that the minimum weight vertex cover problem is solvable in polynomial time with the decomposition strategy. This class is a generalization of the class of triangulated graphs and it contains also a family of not perfect graphs, the circular arc graphs.