Tiling edge-ordered graphs with monotone paths and other structures

Given graphs and , a perfect -tiling in is a collection of vertex-disjoint copies of in that together cover all the vertices in . The study of the minimum degree threshold forcing a perfect -tiling in a graph 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 . In this paper we initiate the study of the analogous question for edge-ordered graphs. In particular, we characterize for which edge-ordered graphs this problem is well-defined. We also apply the absorbing method to asymptotically determine the minimum degree threshold for forcing a perfect -tiling in an edge-ordered graph, where is any fixed monotone path