Edge-disjoint odd cycles in planar graphs

Authors:
Daniel Král;Heinz-Jürgen Voss
Affiliations:
Department of Applied Mathematics and Institute for Theoretical Computer Science, Charles University, Malostranské námesti 25, 118 00 Prague 1, Czech Republic;Institute of Algebra, Technical University, Dresden, Germany
Venue:
Journal of Combinatorial Theory Series B
Year:
2004

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Abstract

We prove τodd(G) ≤ 2Vodd(G) for each planar graph G where vodd(G) is the maximum number of edge-disjoint odd cycles and τodd(G) is the minimum number of edges whose removal makes G bipartite, i.e. which meet all the odd cycles. For each k, there is a 3- connected planar graph Gk with τodd(Gk) = 2k and vodd(Gk) = k.