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Algorithmic aspects of the generalized clique-transversal problem on chordal graphs. (English) Zbl 0854.68072
Summary: Suppose $$G = (V,E)$$ is a graph in which each maximal clique $$C_i$$ is associated with an integer $$r_i$$, where $$0 \leq r_i \leq |C_i |$$. The generalized clique transversal problem is to determine the minimum cardinality of a subset $$D$$ of $$V$$ such that $$|D \cap C_i |\geq r_i$$ for every maximal clique $$C_i$$ of $$G$$. The problem includes the clique-transversal problem, the $$i,1$$ clique-cover problem, and for perfect graphs, the maximum $$q$$-colorable subgraph problems as special cases. This paper gives complexity results for the problem on subclasses of chordal graphs, e.g., strongly chordal graphs, $$k$$-trees, split graphs, and undirected path graphs.
Reviewer: Reviewer (Berlin)

##### MSC:
 68R10 Graph theory (including graph drawing) in computer science 05C35 Extremal problems in graph theory 05C15 Coloring of graphs and hypergraphs 05C85 Graph algorithms (graph-theoretic aspects) 05C05 Trees
##### Keywords:
clique transversal problem; chordal graphs
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