Long cycles in 3-connected graphs in orientable surfaces

Authors:
Laura Sheppardson;Xingxing Yu
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332E;School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332E
Venue:
Journal of Graph Theory
Year:
2002

Citing 0
Cited 3

The circumference of a graph with no K3,t-minor

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Circumference of 3-connected claw-free graphs and large Eulerian subgraphs of 3-edge-connected graphs

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The circumference of a graph with no K3,t-minor, II

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Abstract

In this article, we apply a cutting theorem of Thomassen to show that there is a function f: N → N such that if G is a 3-connected graph on n vertices which can be embedded in the orientable surface of genus g with face-width at least f(g), then G contains a cycle of length at least cnlog32, where c is a constant not dependent on g. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 69–84, 2002 MSC Primary 05C38 and 05C50 Secondary 57M15.