Computation of Hadwiger Number and Related Contraction Problems: Tight Lower Bounds

Fedor V. Fomin, Daniel Lokshtanov, Ivan Mihajlin, Saket Saurabh, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We prove that the Hadwiger number of an n-vertex graph G (the maximum size of a clique minor in G) cannot be computed in time no(n), unless the Exponential Time Hypothesis (ETH) fails. This resolves a well-known open question in the area of exact exponential algorithms. The technique developed for resolving the Hadwiger number problem has a wider applicability. We use it to rule out the existence of no(n)-time algorithms (up to the ETH) for a large class of computational problems concerning edge contractions in graphs.

Original languageEnglish
Article number10
JournalACM Transactions on Computation Theory
Issue number2
StatePublished - 1 Jun 2021


  • Hadwiger number
  • edge contraction problems
  • exact algorithms
  • exponential-time hypothesis

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics


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