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Article Dans Une Revue SIAM Journal on Discrete Mathematics Année : 2013

Obtaining a Bipartite Graph by Contracting Few Edges

Résumé

The BIPARTITE CONTRACTION problem takes as input an n-vertex graph G 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. We show that BIPARTITE CONTRACTION is fixed-parameter tractable when parameterized by k. 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 vertices, 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.

Dates et versions

hal-01178184 , version 1 (17-07-2015)

Identifiants

Citer

Christophe Paul, Pinar Heggernes, Pim van 'T Hof, Daniel Lokshtanov. Obtaining a Bipartite Graph by Contracting Few Edges. SIAM Journal on Discrete Mathematics, 2013, 27 (4), pp.2143-2156. ⟨10.1137/130907392⟩. ⟨hal-01178184⟩
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