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Obtaining a Bipartite Graph by Contracting Few Edges

Pinar Heggerness 1 Pim Van'T Hof 1 Daniel Lokshtanov 1 Christophe Paul 2
2 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We initiate the study of the Bipartite Contraction problem from the perspective of param- eterized 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 Con- traction. 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.
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Submitted on : Wednesday, June 30, 2021 - 1:12:01 PM
Last modification on : Friday, October 22, 2021 - 3:07:30 PM
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Pinar Heggerness, Pim Van'T Hof, Daniel Lokshtanov, Christophe Paul. Obtaining a Bipartite Graph by Contracting Few Edges. IARCS 31st Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2011), Dec 2011, Mumbai, India. pp.217-228, ⟨10.4230/LIPIcs.FSTTCS.2011.217⟩. ⟨lirmm-00805189⟩



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