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Hadwiger Number of Graphs with Small Chordality

  • Petr A. GolovachEmail author
  • Pinar Heggernes
  • Pim van ’t Hof
  • Christophe Paul
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8747)

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 \(s\ge 2\), but is NP-hard on chordal graphs for every fixed \(s\ge 2\).

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Petr A. Golovach
    • 1
    Email author
  • Pinar Heggernes
    • 1
  • Pim van ’t Hof
    • 1
  • Christophe Paul
    • 2
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.CNRSLIRMMMontpellierFrance

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