Contracting a chordal graph to a split graph or a tree

Authors:
Petr A. Golovach;Marcin Kamiński;Daniël Paulusma
Affiliations:
School of Engineering and Computing Sciences, Durham University, Durham, United Kingdom;Département d'Informatique, Université Libre de Bruxelles, Belgium;School of Engineering and Computing Sciences, Durham University, Durham, United Kingdom
Venue:
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Year:
2011

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Abstract

The problems CONTRACTIBILITY and INDUCED MINOR are to test whether a graph G contains a graph H as a contraction or as an induced minor, respectively. We show that these two problems can be solved in |VG|f(|VH|) time if G is a chordal input graph and H is a split graph or a tree. In contrast, we show that containment relations extending SUBGRAPH ISOMORPHISM can be solved in linear time if G is a chordal input graph and H is an arbitrary graph not part of the input.