Hadwiger Number of Graphs with Small Chordality

Petr A. Golovach, Pinar Heggernes, Pim van 't Hof, Christophe Paul
2015 SIAM Journal on Discrete Mathematics  
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
more » ... blem 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.
doi:10.1137/140975279 fatcat:5w6bkeixprhctnjopisjxg3c3e