Journal of Combinatorics

Volume 8 (2017)

Number 2

Cycle double covers and long circuits of graphs

Pages: 341 – 347

DOI: http://dx.doi.org/10.4310/JOC.2017.v8.n2.a6

Authors

Xiaofeng Wang (Department of Mathematics and Actuarial Science, Indiana University Northwest, Gary, In., U.S.A.)

Rui Xu (Department of Mathematics, University of West Georgia, Carrollton, Ga., U.S.A.)

Dong Ye (Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, Tenn., U.S.A.)

Abstract

The 5-Cycle Double Cover Conjecture claims that every bridgeless graph has a cycle double cover which consists of at most 5 cycles. In this paper, we prove that if a cubic graph has a long circuit, then it has a 5-cycle double cover. Our main theorem partially strengthens some previously known results.

Keywords

cycle double covers, $k$-cycle double covers, strong cycle double covers

2010 Mathematics Subject Classification

05C38

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Published 14 February 2017