On Multicolor Turán Numbers

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-08-26 DOI:10.1137/24m1639488

József Balogh, Anita Liebenau, Letícia Mattos, Natasha Morrison

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 3, Page 2297-2311, September 2024.
Abstract. We address a problem which is a generalization of Turán-type problems recently introduced by Imolay, Karl, Nagy, and Váli. Let [math] be a fixed graph and let [math] be the union of [math] edge-disjoint copies of [math], namely [math], where each [math] is isomorphic to a fixed graph [math] and [math] for all [math]. We call a subgraph [math] multicolored if [math] and [math] share at most one edge for all [math]. Define [math] to be the maximum value [math] such that there exists [math] on [math] vertices without a multicolored copy of [math]. We show that [math] and that all extremal graphs are close to a blow-up of the 5-cycle. This bound is tight up to the linear error term.

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关于多色图兰数字

SIAM 离散数学杂志》，第 38 卷第 3 期，第 2297-2311 页，2024 年 9 月。摘要。我们要解决的问题是伊莫莱、卡尔、纳吉和瓦利最近提出的图兰型问题的一般化。设 [math] 是一个固定图，[math] 是 [math] 边缘相交的副本的联合，即 [math]，其中每个 [math] 都与一个固定图 [math] 和 [math] 同构。如果[math]和[math]在所有[math]中最多共享一条边，我们就称子图[math]为多色图。定义 [math] 为最大值 [math]，使得 [math] 顶点上存在 [math] 而没有 [math] 的多色副本。我们证明，[math] 以及所有极值图都接近于 5 循环的炸裂。这个约束在线性误差项以内都是紧密的。

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

SIAM Journal on Discrete Mathematics 数学-应用数学

CiteScore

1.90

自引率

0.00%

发文量

124

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Discrete Mathematics (SIDMA) publishes research papers of exceptional quality in pure and applied discrete mathematics, broadly interpreted. The journal''s focus is primarily theoretical rather than empirical, but the editors welcome papers that evolve from or have potential application to real-world problems. Submissions must be clearly written and make a significant contribution. Topics include but are not limited to: properties of and extremal problems for discrete structures combinatorial optimization, including approximation algorithms algebraic and enumerative combinatorics coding and information theory additive, analytic combinatorics and number theory combinatorial matrix theory and spectral graph theory design and analysis of algorithms for discrete structures discrete problems in computational complexity discrete and computational geometry discrete methods in computational biology, and bioinformatics probabilistic methods and randomized algorithms.