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Communication Dans Un Congrès Année : 2014

Hadwiger Number of Graphs with Small Chordality

Résumé

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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Dates et versions

hal-01178217 , version 1 (04-02-2020)

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Citer

Petr A. Golovach, Pinar Heggernes, Pim van 'T Hof, Christophe Paul. Hadwiger Number of Graphs with Small Chordality. WG 2014 - 40th International Workshop on Graph-Theoretic Concepts in Computer Science, Jun 2014, Nouan-le-Fuzelier, France. pp.201-213, ⟨10.1007/978-3-319-12340-0_17⟩. ⟨hal-01178217⟩
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