Increasing the minimum degree of a graph by contractions

Petr A. Golovach, Marcin Kamiński, Daniël Paulusma, Dimitrios M. Thilikos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The Degree Contractibility problem is to test whether a given graph G can be modified to a graph of minimum degree at least d by using at most k contractions. We prove the following three results. First, Degree Contractibility is NP-complete even when d = 14. Second, it is fixed-parameter tractable when parameterized by k and d. Third, it is W[1]-hard when parameterized by k. We also study its variant where the input graph is weighted, i.e., has some edge weighting and the contractions preserve these weights. The Weighted Degree Contractibility problem is to test if a weighted graph G can be contracted to a weighted graph of minimum weighted degree at least d by using at most k weighted contractions. We show that this problem is NP-complete and that it is fixed-parameter tractable when parameterized by k.

Original languageEnglish (US)
Title of host publicationParameterized and Exact Computation - 6th International Symposium, IPEC 2011, Revised Selected Papers
Pages67-79
Number of pages13
DOIs
StatePublished - 2012
Event6th International Symposium on Parameterized and Exact Computation, IPEC 2011 - Saarbrucken, Germany
Duration: Sep 6 2011Sep 8 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7112 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference6th International Symposium on Parameterized and Exact Computation, IPEC 2011
Country/TerritoryGermany
CitySaarbrucken
Period9/6/119/8/11

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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