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

Mengyu Duan; Zhiwei Guo; Binlong Li; Shenggui Zhang

doi:10.1016/j.disc.2025.114507

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

Mengyu Duan, Zhiwei Guo, Binlong Li, Shenggui Zhang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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≤k≤|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.

Original language	English
Article number	114507
Journal	Discrete Mathematics
Volume	348
Issue number	8
DOIs	https://doi.org/10.1016/j.disc.2025.114507
State	Published - Aug 2025

Keywords

Arc-colored digraph
Color number
Proper even pancyclicity
Proper hamiltonicity
Proper pancyclicity

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10.1016/j.disc.2025.114507

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abstract = "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≤k≤|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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AU - Zhang, Shenggui

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AB - 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≤k≤|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.

KW - Arc-colored digraph

KW - Color number

KW - Proper even pancyclicity

KW - Proper hamiltonicity

KW - Proper pancyclicity

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

Abstract

Keywords

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