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arXiv · 1406.3812

Hadwiger number of graphs with small chordality

Petr A. Golovach·Pinar Heggernes·Pim van 't Hof·Christophe Paul
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Abstract

The Hadwiger number of a graph G is the largest integer h such that G has the complete graph K_h as a minor. We show that the problem of determining the Hadwiger number of a graph is NP-hard on co-bipartite graphs, but can be solved in polynomial time on cographs and on bipartite permutation graphs. We also consider a natural generalization of this problem that asks for the largest integer h such that G has a minor with h vertices and diameter at most $s$. We show that this problem can be solved in polynomial time on AT-free graphs when s>=2, but is NP-hard on chordal graphs for every fixed s>=2.

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BibTeXRIS

Petr A. Golovach, Pinar Heggernes, Pim van 't Hof, Christophe Paul. 2014-06-15. Hadwiger number of graphs with small chordality. https://arxiv.org/abs/1406.3812

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