Spanning cycles in regular matroids without M*(K5) minors

Authors:
Hong-Jian Lai;Bolian Liu;Yan Liu;Yehong Shao
Affiliations:
Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA and School of Mathematics, Physics and Software Enginneering, Lanzhou Jiaotong University, Lanzhou 730070, PR China;Department of Mathematics, South China Normal University, Guangzhou, PR China;Department of Mathematics, South China Normal University, Guangzhou, PR China;Arts and Sciences, Ohio University Southern, Ironton, OH 45638, USA
Venue:
European Journal of Combinatorics
Year:
2008

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Abstract

Catlin and Jaeger proved that the cycle matroid of a 4-edge-connected graph has a spanning cycle. This result can not be generalized to regular matroids as there exist infinitely many connected cographic matroids, each of which contains a M^*(K"5) minor and has arbitrarily large cogirth, that do not have spanning cycles. In this paper, we proved that if a connected regular matroid without a M^*(K"5)-minor has cogirth at least 4, then it has a spanning cycle.