文章基本信息

标题：Obtaining a Bipartite Graph by Contracting Few Edges
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作者：Pinar Heggernes ; Pim van 't Hof ; Daniel Lokshtanov 等
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2011
卷号：13
页码：217-228
DOI：10.4230/LIPIcs.FSTTCS.2011.217
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：fixed parameter tractability; graph modification problems; edge contractions; bipartite graphs