广义Mycielski图中的Hamilton环

IF 0.6 Q4 MATHEMATICS, APPLIED

Discrete Mathematics Algorithms and Applications Pub Date : 2023-10-17 DOI:10.1142/s179383092350088x

L. Panneerselvam, S. Ganesamurthy, A. Muthusamy

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引用次数: 0

摘要

设[公式:见文]表示[公式:见文]的广义Mycielski图。本文证明了对于[公式:见文]，若[公式:见文]存在[公式:见文]对边不相交的汉密尔顿环，则[公式:见文]存在[公式:见文]对边不相交的汉密尔顿环。此外,结果表明,如果[公式:看到文本][公式:看到文本]成对edge-disjoint汉密尔顿周期与[公式:看到文本][公式:看到文本]和[公式:看到文本][公式:看到文本),然后(公式:看到文本)(公式:看到文本)成对edge-disjoint汉密尔顿周期。最后证明，即使[公式:见文]是具有特定[公式:见文]因子的非哈密顿函数，[公式:见文]也是哈密顿函数。因此，Flower - Snark图的Mycielski图(公式:见文)对于所有奇数(公式:见文)都是汉密尔顿图。

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Hamilton cycles in Generalized Mycielski Graphs

Let [Formula: see text] denote the generalized Mycielski graph of [Formula: see text]. In this paper, it is proved that for [Formula: see text], if [Formula: see text] has [Formula: see text] pairwise edge-disjoint Hamilton cycles, then [Formula: see text] has [Formula: see text] Hamilton cycles which are pairwise edge-disjoint. Further, it is shown that if [Formula: see text] has [Formula: see text] pairwise edge-disjoint Hamilton cycles with [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text], then [Formula: see text] has [Formula: see text] pairwise edge-disjoint Hamilton cycles. Finally it is shown that [Formula: see text] is hamiltonian even when [Formula: see text] is non-hamiltonian with a specified [Formula: see text]-factor. Consequently, the Mycielski graph of Flower Snark graph [Formula: see text], for all odd [Formula: see text], is Hamiltonian.

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来源期刊

Discrete Mathematics Algorithms and Applications MATHEMATICS, APPLIED-

CiteScore

1.50

自引率

41.70%

发文量

129