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Finding odd cycle transversals. (English) Zbl 1052.05061
Summary: We present an $$O(mn)$$ algorithm to determine whether a graph $$G$$ with $$m$$ edges and $$n$$ vertices has an odd cycle transversal of order at most $$k$$, for any fixed $$k$$. We also obtain an algorithm that determines, in the same time, whether a graph has a half integral packing of odd cycles of weight $$k$$.

##### MSC:
 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C38 Paths and cycles
##### Keywords:
Odd cycle transversal; Odd cycle packing; Bipartite graph
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##### References:
 [1] Karp, R., Reducibility among combinatorial problems, (), 85-103 · Zbl 0366.68041 [2] Reed, B., Mangoes and blueberries, Combinatorica, 19, 2, 267-296, (1999) · Zbl 0928.05059 [3] R. Rizzi, V. Bafna, S. Istrail, G. Lancia, Practical algorithms and fixed-parameter tractability for the single individual SNP haplotyping problem, Algorithms in Bioinformatics: Second International Workshop, Lecture Notes in Computer Science, Vol. 2452, Springer, Berlin, 2002, pp. 29-43. · Zbl 1016.68685 [4] Robertson, N.; Seymour, P., Graph minors. XIII. the disjoint paths problem, J. combin. theory ser. B, 63, 1, 65-110, (1995) · Zbl 0823.05038
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