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Obtaining a Bipartite Graph by Contracting Few Edges Heggernes, Pinar van 't Hof, Pim Lokshtanov, Daniel Paul, Christophe fixed parameter tractability graph modification problems edge contractions bipartite graphs We initiate the study of the Bipartite Contraction problem from the perspective of parameterized complexity. In this problem we are given a graph G on n vertices and an integer k, and the task is to determine whether we can obtain a bipartite graph from G by a sequence of at most k edge contractions. Our main result is an f(k) n^{O(1)} time algorithm for Bipartite Contraction. Despite a strong resemblance between Bipartite Contraction and the classical Odd Cycle Transversal (OCT) problem, the methods developed to tackle OCT do not seem to be directly applicable to Bipartite Contraction. To obtain our result, we combine several techniques and concepts that are central in parameterized complexity: iterative compression, irrelevant vertex, and important separators. To the best of our knowledge, this is the first time the irrelevant vertex technique and the concept of important separators are applied in unison. Furthermore, our algorithm may serve as a comprehensible example of the usage of the irrelevant vertex technique. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Pinar Heggernes and Pim van 't Hof and Daniel Lokshtanov and Christophe Paul 2011 Is Part Of LIPIcs, Volume 13, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.FSTTCS.2011.217 urn:nbn:de:0030-drops-33579 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2011.217 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode