圆弧色完全二部有向图和完全二部有向图中的适当着色C4→s

IF 0.7 3区数学 Q2 MATHEMATICS Discrete Mathematics Pub Date : 2025-04-01 Epub Date: 2024-12-17 DOI:10.1016/j.disc.2024.114367

Mengyu Duan , Binlong Li , Shenggui Zhang

引用次数: 0

摘要

如果一个有向图的每个连续的弧都有不同的颜色，那么它的子图就被称为有向图。设D是有向图。对于有向图H，设pc（D，H）为满足每个c(D)≥pc（D，H）的弧色有向图DC包含H的适当彩色副本的最小值，其中c(D)为DC的颜色数。设Kn↔和Km，n↔分别是由完全图Kn和完全二部图Km，n通过用一对对称弧（u,v）和（v,u）代替每条边uv得到的有向图；并设Ck→为长度为k的有向循环。本文确定了pc（Kn↔，C4→）、pc（Km,n↔，C4→）并描述了有向图的相应的极值弧着色。

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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Properly colored C4→'s in arc-colored complete and complete bipartite digraphs

A subdigraph of an arc-colored digraph is called properly colored if its every consecutive arcs have distinct colors. Let D be a digraph. For a digraph H, let

p c (D, H)

be the minimum number such that every arc-colored digraph

D^{C}

with

c (D) \geq p c (D, H)

contains a properly colored copy of H, where

c (D)

is the number of colors of

D^{C}

. Let

\overset{\leftrightarrow}{K_{n}}

and

\overset{\leftrightarrow}{K_{m, n}}

be the digraphs obtained from the complete graph

K_{n}

and the complete bipartite graph

K_{m, n}

respectively by replacing each edge uv with a pair of symmetric arcs

(u, v)

and

(v, u)

; and let

\vec{C_{k}}

be the directed cycle of length k. In this paper we determine

p c (\overset{\leftrightarrow}{K_{n}}, \vec{C_{4}})

p c (\overset{\leftrightarrow}{K_{m, n}}, \vec{C_{4}})

and characterize the corresponding extremal arc-colorings of 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.

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