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A new class for large sets of almost Hamilton cycle decompositions

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Abstract

A k-cycle system of order v with index λ, denoted by CS(v, k, λ), is a collection A of k-cycles (blocks) of K v such that each edge in K v appears in exactly λ blocks of A. A large set of CS(v, k, λ)s is a partition of the set of all k-cycles of K v into CS(v, k, λ)s, and is denoted by LCS(v, k, λ). A (v −1)-cycle in K v is called almost Hamilton. The completion of the existence problem for LCS(v, v−1, λ) depends only on one case: all v ≥ 4 for λ = 2. In this paper, it is shown that there exists an LCS(v, v − 1, 2) for all v ≡ 2 (mod 4), v ≥ 6.

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Authors and Affiliations

  1. School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China

    Hong-tao Zhao

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  1. Hong-tao Zhao
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Correspondence to Hong-tao Zhao.

Additional information

Supported in part by the National Natural Science Foundation of China (No. 10901051,11201143), the Fundamental Research Funds for the Central Universities (No.2016MS66) and the Co-construction Project of Bejing Municipal Commission of Education.

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Zhao, Ht. A new class for large sets of almost Hamilton cycle decompositions. Acta Math. Appl. Sin. Engl. Ser. 33, 865–870 (2017). https://doi.org/10.1007/s10255-017-0703-0

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  • DOI: https://doi.org/10.1007/s10255-017-0703-0

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