用单调路径和其他结构平铺边缘有序图

Pub Date : 2024-06-07 DOI:10.1137/23m1572519

Igor Araujo, Simón Piga, Andrew Treglown, Zimu Xiang

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引用次数: 0

摘要

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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Tiling Edge-Ordered Graphs with Monotone Paths and Other Structures

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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