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Ordered Gallai–Ramsey numbers

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Discrete Applied Mathematics Pub Date : 2025-06-23 DOI:10.1016/j.dam.2025.06.018

Yaping Mao

引用次数: 0

Abstract

An ordered graph is a pair

(G, A)

where

A

is an ordering of

V (G)

of a graph

G

. For given ordered graphs

(G, A), (H_{1}, A_{1}), (H_{2}, A_{2}), \dots, (H_{k}, A_{k})

, the ordered Gallai–Ramsey number

{\bar{g r}}_{k} ((G, A) : (H_{1}, A_{1}), (H_{2}, A_{2}), \dots, (H_{k}, A_{k}))

is defined as the smallest number

N

such that every

k

-edge-coloring of

K_{N}

contains an order preserving rainbow copy of

(G, A)

or an order preserving monochromatic copy of

(H_{i}, A_{i})

with color

i

as an ordered subgraph. In this paper, we first studied the ordered complete graphs without small rainbow subgraphs, like stars, paths, and matchings. Next, we give the exact values or bounds for the ordered Gallai–Ramsey numbers.

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对于给定的有序图（G, a），（H1,A1），（H2,A2），…，（Hk,Ak），有序galai - ramsey数gr¯k((G, a):(H1,A1),（H2,A2)，…，（Hk,Ak））定义为最小的数N，使得KN的每k边着色都包含（G, a）的保序彩虹副本或（Hi,Ai）的保序单色副本，颜色i为有序子图。在本文中，我们首先研究了没有小彩虹子图，如星星、路径和匹配的有序完全图。接下来，我们给出有序Gallai-Ramsey数的确切值或边界。

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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来源期刊

Discrete Applied Mathematics 数学-应用数学

CiteScore

2.30

自引率

9.10%

发文量

422

审稿时长

4.5 months

期刊介绍： The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal. Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.