# Obtaining a Bipartite Graph by Contracting Few Edges

@article{Heggernes2011ObtainingAB,
title={Obtaining a Bipartite Graph by Contracting Few Edges},
author={Pinar Heggernes and Pim van 't Hof and Daniel Lokshtanov and Christophe Paul},
journal={SIAM J. Discret. Math.},
year={2011},
volume={27},
pages={2143-2156}
}
• Published 26 February 2011
• Mathematics
• SIAM J. Discret. Math.
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…
44 Citations

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### On the Hardness of Eliminating Small Induced Subgraphs by Contracting Edges

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### Split Contraction

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### Parameterized Complexity of Two Edge Contraction Problems with Degree Constraints

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Two graph modification problems where the goal is to obtain a graph whose vertices satisfy certain degree constraints are studied, and it is proved that both problems to be NP-complete for any fixed d ≥ 2.

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