少数单色有界度图的平铺边彩色图

IF 1 2区数学 Q1 MATHEMATICS

Combinatorica Pub Date : 2023-11-21 DOI:10.1007/s00493-023-00072-1

Jan Corsten, Walner Mendonça

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引用次数: 2

摘要

我们证明，对于所有整数\(\Delta ,r \ge 2\)，存在一个常数\(C = C(\Delta ,r) >0\)，使得对于含有\(v(F_n) = n\)和\(\Delta (F_n) \le \Delta \)的图的每一个序列\({\mathcal {F}}= \{F_1, F_2, \ldots \}\)，对于每一个\(n \in {\mathbb {N}}\)，都成立如下式。在每个r边颜色的\(K_n\)中，有一个来自\({\mathcal {F}}\)的最多C个单色副本的集合，其顶点集分区为\(V(K_n)\)。这在Grinshpun和Sárközy的猜想上取得了进展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Tiling Edge-Coloured Graphs with Few Monochromatic Bounded-Degree Graphs

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Tiling Edge-Coloured Graphs with Few Monochromatic Bounded-Degree Graphs

We prove that for all integers \(\Delta ,r \ge 2\), there is a constant \(C = C(\Delta ,r) >0\) such that the following is true for every sequence \({\mathcal {F}}= \{F_1, F_2, \ldots \}\) of graphs with \(v(F_n) = n\) and \(\Delta (F_n) \le \Delta \), for each \(n \in {\mathbb {N}}\). In every r-edge-coloured \(K_n\), there is a collection of at most C monochromatic copies from \({\mathcal {F}}\) whose vertex-sets partition \(V(K_n)\). This makes progress on a conjecture of Grinshpun and Sárközy.

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来源期刊

Combinatorica 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： COMBINATORICA publishes research papers in English in a variety of areas of combinatorics and the theory of computing, with particular emphasis on general techniques and unifying principles. Typical but not exclusive topics covered by COMBINATORICA are - Combinatorial structures (graphs, hypergraphs, matroids, designs, permutation groups). - Combinatorial optimization. - Combinatorial aspects of geometry and number theory. - Algorithms in combinatorics and related fields. - Computational complexity theory. - Randomization and explicit construction in combinatorics and algorithms.