The Hadwiger number of a graph G is the largest integer h such that G has the complete graph Kh 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.
CITATION STYLE
Golovach, P. A., Heggernes, P., van ’t Hof, P., & Paul, C. (2014). Hadwiger number of graphs with small chordality. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8747, pp. 201–213). Springer Verlag. https://doi.org/10.1007/978-3-319-12340-0_17
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