@inproceedings{c69a402796974fe680c3a9543b05a42f,
title = "Computation of Hadwiger number and related contraction problems: Tight lower bounds",
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 ETH) for a large class of computational problems concerning edge contractions in graphs.",
keywords = "Edge Contraction Problems, Exact Algorithms, Exponential-Time Hypothesis, Hadwiger Number",
author = "Fomin, {Fedor V.} and Daniel Lokshtanov and Ivan Mihajlin and Saket Saurabh and Meirav Zehavi",
note = "Publisher Copyright: {\textcopyright} Fedor V. Fomin, Daniel Lokshtanov, Ivan Mihajlin, Saket Saurabh, and Meirav Zehavi; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).; 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020 ; Conference date: 08-07-2020 Through 11-07-2020",
year = "2020",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.ICALP.2020.49",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
editor = "Artur Czumaj and Anuj Dawar and Emanuela Merelli",
booktitle = "47th International Colloquium on Automata, Languages, and Programming, ICALP 2020",
address = "Germany",
}