Speaker: Igor Albuquerque Araujo
Title: Edge-ordered graphs and perfect tilings
Abstract: Given graphs F and G, a perfect F-tiling in G is a collection of vertex-disjoint copies of F in G that together cover all the vertices in G. The study of the minimum degree threshold forcing a perfect F-tiling in a graph G has a long history, culminating in the Kühn–Osthus theorem [Combinatorica 2009] which resolves this problem, up to an additive constant, for all graphs F. In this ongoing work, we initiate the study of the analogous question for edge-ordered graphs. In particular, we characterize for which edge-ordered graphs F this problem is well-defined. We also apply the absorbing method to asymptotically determine the minimum degree threshold for forcing a perfect P-tiling in an edge-ordered graph, where P is any fixed monotone path. This is a joint work with Simón Piga, Andrew Treglown and Zimu Xiang.
