关于圆弧色完全（平衡二部）有向图的适当哈密性和适当（偶）环性

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-04-03 DOI:10.1016/j.disc.2025.114507

Mengyu Duan , Zhiwei Guo , Binlong Li , Shenggui Zhang

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引用次数: 0

摘要

如果一个有向图的每一对连续的弧都有不同的颜色，那么这个有向图的子图就被称为有向图。我们称一个弧色有向图D为适当的哈密顿图，如果它包含一个适当的有色哈密顿环，如果它包含一个长度为k的适当的（偶）环，对于2≤k≤|V(D)|，我们称它为适当的（偶）环。本文首先得到了弧色完全（平衡二部）有向图的适当色Hamilton环存在的一些色数条件，并进一步证明了这些条件仍能保证弧色完全（平衡二部）有向图的（偶）泛环性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On proper hamiltonicity and proper (even) pancyclicity of arc-colored complete (balanced bipartite) digraphs

A subdigraph of an arc-colored digraph is called properly colored if its every pair of consecutive arcs have distinct colors. We call an arc-colored digraph D properly hamiltonian if it contains a properly colored Hamilton cycle, and properly (even) pancyclic if it contains a properly colored cycle of length k for every (even) k with

2 \leq k \leq | V (D) |

. In this paper, we first obtain some color number conditions for the existence of properly colored Hamilton cycles of arc-colored complete (balanced bipartite) digraphs, and further prove that the these conditions can still guarantee the (even) pancyclicity of arc-colored complete (balanced bipartite) digraphs.

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.