Igor Araujo, Simón Piga, Andrew Treglown, Zimu Xiang
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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.
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.
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