Article

# Min-max relations for odd cycles in planar graphs

08/2011;
Source: arXiv

ABSTRACT Let m(G) be the maximum number of vertex-disjoint odd cycles of a graph G and
t(G) the minimum number of vertices whose removal makes G bipartite. We show
that t(G)<=6m(G) if G is planar. This improves the previous bound t(G)<=10m(G)
by Fiorini, Hardy, Reed and Vetta [Math. Program. Ser. B 110 (2007), 71-91].

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### Keywords

Fiorini

G bipartite

graph G

maximum number

vertex-disjoint odd cycles

vertices

Vetta [Math