Abstract
Let G = ( V, E) be a graph with a positive number wt( v) assigned to each v ϵ v. A weighted clique cover of the vertices of G is a collection of cliques with a non-negative weight y c assigned to each clique C in the collection such that σ C: vϵ C Y C ⩾wt( v) for all v ϵ V. The problem considered is to minimize σ C y C over all weighted clique covers. A polynomial time algorithm for this problem is presented for graphs that are claw-free and perfect.
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