eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-29
49:1
49:18
10.4230/LIPIcs.ICALP.2020.49
article
Computation of Hadwiger Number and Related Contraction Problems: Tight Lower Bounds
Fomin, Fedor V.
1
Lokshtanov, Daniel
2
Mihajlin, Ivan
3
Saurabh, Saket
4
5
Zehavi, Meirav
6
University of Bergen, Norway
University of California, Santa Barbara, CA, USA
University of California, San Diego, CA, USA
Department of Informatics, University of Bergen, Norway
The Institute of Mathematical Sciences, Chennai, India
Ben-Gurion University of the Negev, Beer-Sheva, Israel
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 n^o(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 n^o(n)-time algorithms (up to ETH) for a large class of computational problems concerning edge contractions in graphs.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol168-icalp2020/LIPIcs.ICALP.2020.49/LIPIcs.ICALP.2020.49.pdf
Hadwiger Number
Exponential-Time Hypothesis
Exact Algorithms
Edge Contraction Problems