Abstract
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 language | American English |
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Article number | 10 |
Journal | ACM Transactions on Computation Theory |
Volume | 13 |
Issue number | 2 |
DOIs | |
State | Published - 1 Jun 2021 |
Keywords
- Hadwiger number
- edge contraction problems
- exact algorithms
- exponential-time hypothesis
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computational Theory and Mathematics