Combinatorial Problems on H-graphs

Steven Chaplick; Peter Zeman

doi:10.1016/J.ENDM.2017.06.042

Combinatorial Problems on H-graphs

Steven Chaplick^*
, Peter Zeman^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

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. Whe 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.

Original language	English
Pages (from-to)	223-229
Number of pages	7
Journal	Electronic Notes in Discrete Mathematics
Volume	61
DOIs	https://doi.org/10.1016/J.ENDM.2017.06.042
Publication status	Published - 2017
Externally published	Yes

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10.1016/J.ENDM.2017.06.042

1 Article
1 Preprint

On H-Topological Intersection Graphs
Chaplick, S., Topfer, M., Vobornik, J. & Zeman, P., Nov 2021, In: Algorithmica. 83, 11, p. 3281-3318 38 p.
Research output: Contribution to journal › Article › Academic › peer-review
Combinatorial Problems on $H$-graphs
Chaplick, S. & Zeman, P., 2017, 10 p.
Research output: Working paper / Preprint › Preprint

Cite this

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title = "Combinatorial Problems on H-graphs",

abstract = "Bir{\'o}, 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. Whe 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.",

author = "Steven Chaplick and Peter Zeman",

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PY - 2017

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N2 - 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. Whe 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.

AB - 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. Whe 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.

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DO - 10.1016/J.ENDM.2017.06.042

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VL - 61

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EP - 229

JO - Electronic Notes in Discrete Mathematics

JF - Electronic Notes in Discrete Mathematics

ER -

Combinatorial Problems on H-graphs

Abstract

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Research output

On H-Topological Intersection Graphs

Combinatorial Problems on $H$-graphs

Cite this