Approximate min-max relations for odd cycles in planar graphs

Authors:
Samuel Fiorini;Nadia Hardy;Bruce Reed;Adrian Vetta
Affiliations:
,GERAD, Montreal, Quebec, Canada;McGill University, Montreal, Quebec, Canada;McGill University, Montreal, Quebec, Canada;McGill University, Montreal, Quebec, Canada
Venue:
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Year:
2005

Citing 2
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The four-colour theorem

Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Edge-disjoint odd cycles in planar graphs

Journal of Combinatorial Theory Series B

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Abstract

We study the ratio between the minimum size of an odd cycle vertex transversal and the maximum size of a collection of vertex-disjoint odd cycles in a planar graph. We show that this ratio is at most 10. For the corresponding edge version of this problem, Král and Voss [7] recently proved that this ratio is at most 2; we also give a short proof of their result.