Tiling Edge-Ordered Graphs with Monotone Paths and Other Structures

IF 0.9 3区数学 Q2 MATHEMATICS

SIAM Journal on Discrete Mathematics Pub Date : 2024-06-07 DOI:10.1137/23m1572519

Igor Araujo, Simón Piga, Andrew Treglown, Zimu Xiang

引用次数: 0

Abstract

SIAM Journal on Discrete Mathematics, Volume 38, Issue 2, Page 1808-1839, June 2024.
Abstract. Given graphs [math] and [math], a perfect [math]-tiling in [math] is a collection of vertex-disjoint copies of [math] in [math] that together cover all the vertices in [math]. The study of the minimum degree threshold forcing a perfect [math]-tiling in a graph [math] has a long history, culminating in the Kühn–Osthus theorem [D. Kühn and D. Osthus, Combinatorica, 29 (2009), pp. 65–107] which resolves this problem, up to an additive constant, for all graphs [math]. In this paper we initiate the study of the analogous question for edge-ordered graphs. In particular, we characterize for which edge-ordered graphs [math] this problem is well-defined. We also apply the absorbing method to asymptotically determine the minimum degree threshold for forcing a perfect [math]-tiling in an edge-ordered graph, where [math] is any fixed monotone path.

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用单调路径和其他结构平铺边缘有序图

SIAM 离散数学杂志》第 38 卷第 2 期第 1808-1839 页，2024 年 6 月。摘要。给定图[math]和[math]，[math]中的完美[math]-簇是[math]中[math]的顶点相交副本的集合，这些副本共同覆盖了[math]中的所有顶点。关于图[math]中强制完美[math]-tiling的最小度阈值的研究由来已久，库恩-奥斯特胡斯定理（Kühn-Osthus theorem）[D. Kühn and D. Osthus, Combinatorica, 29 (2009), pp.］在本文中，我们开始研究边缘有序图的类似问题。特别是，我们描述了对于哪些边缘有序图[math]，这个问题是定义明确的。我们还应用吸收法渐近地确定了在边缘有序图中强迫完美[math]倾斜的最小度阈值，其中[math]是任何固定的单调路径。

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.