Abstract
In 1985, Alon and Tarsi conjectured that the length of a shortest cycle cover of a bridgeless graph H is at most 7/5 |E(H|). The conjecture is still open. Let G be a 2-edge-connected graph embedded with face-width k on the non-spherical orientable surface S g . We give an upper bound on the length of a cycle cover of G. In particular, if g = 1 and k ≥ 48, or g = 2 and k ≥ 427, or g ≥ 3 and k ≥ 288(4g - 1), then the upper bound is 7/5 |E(G|), which means that Alon and Tarsi’s conjecture holds for such a graph.
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corresponding author and supported by NNSFC under the granted number 11171114.
supported by NNSFC under the granted number 11171114.
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Ma, D., Ren, H. A cycle cover of a 2-edge-connected graph embedded with large face-width on an orientable surface. Isr. J. Math. 212, 219–235 (2016). https://doi.org/10.1007/s11856-016-1297-6
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DOI: https://doi.org/10.1007/s11856-016-1297-6