Recognizing the P_4-structure of claw-free graphs and a larger graph class
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International audience The P_4-structure of a graph G is a hypergraph \textbfH on the same vertex set such that four vertices form a hyperedge in \textbfH whenever they induce a P_4 in G. We present a constructive algorithm which tests in polynomial time whether a given 4-uniform hypergraph is the P_4-structure of a claw-free graph and of (banner,chair,dart)-free graphs. The algorithm relies on new structural results for (banner,chair,dart)-free graphs which are based on the concept of p-connectedness. As a byproduct, we obtain a polynomial time criterion for perfectness for a large class of graphs properly containing claw-free graphs.
2009 ◽
Vol Vol. 11 no. 2
(Graph and Algorithms)
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2013 ◽
Vol Vol. 15 no. 2
(Combinatorics)
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2014 ◽
Vol Vol. 16 no. 3
(Graph Theory)
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2015 ◽
Vol Vol. 17 no. 1
(Graph Theory)
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Keyword(s):
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2012 ◽
Vol DMTCS Proceedings vol. AQ,...
(Proceedings)
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