Luitpold Babel ; Andreas Brandstädt ; Van Bang Le - Recognizing the P_4-structure of claw-free graphs and a larger graph class

dmtcs:294 - Discrete Mathematics & Theoretical Computer Science, January 1, 2002, Vol. 5 - https://doi.org/10.46298/dmtcs.294
Recognizing the P_4-structure of claw-free graphs and a larger graph classArticle

Authors: Luitpold Babel 1; Andreas Brandstädt 2; Van Bang Le

  • 1 Zentrum Mathematik [Munchen]
  • 2 Institut für Informatik [Rostock]

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.


Volume: Vol. 5
Published on: January 1, 2002
Imported on: March 26, 2015
Keywords: perfect graphs.,p-connected graphs,homogeneous set,perfect graphs,Claw-free graphs,reconstruction problem,P_4-structure,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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