Combinatorial Problems on H-graphs

Biró, Hujter, and Tuza introduced the concept of H-graphs (1992), intersection graphs of connected subgraphs of a subdivision of a fixed graph H. They naturally generalize many important classes of graphs. We continue their study by considering coloring, clique, and isomorphism problems. We show tha...

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Bibliographic Details
Published inElectronic notes in discrete mathematics Vol. 61; pp. 223 - 229
Main Authors Chaplick, Steven, Zeman, Peter
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2017
Subjects
clique
coloring
intersection graphs
isomorphism
treewidth
intersection graphs
clique
coloring
treewidth
isomorphism
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ISSN1571-0653
1571-0653
DOI10.1016/j.endm.2017.06.042

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Summary:Biró, Hujter, and Tuza introduced the concept of H-graphs (1992), intersection graphs of connected subgraphs of a subdivision of a fixed graph H. They naturally generalize many important classes of graphs. We continue their study by considering coloring, clique, and isomorphism problems. We show that if H contains a certain multigraph as a minor, then H-graphs are GI-complete and the clique problem is APX-hard. Also, when H is a cactus the clique problem can be solved in polynomial time and when a graph G has a Helly H-representation, the clique problem can be solved in polynomial time. We use treewidth to show that both the k-clique and list k-coloring problems are FPT on H-graphs. These results also apply to treewidth-bounded classes where treewidth is bounded by a function of the clique number.
ISSN:1571-0653
1571-0653
DOI:10.1016/j.endm.2017.06.042