TILING EDGE-ORDERED GRAPHS WITH MONOTONE PATHS AND OTHER STRUCTURES.

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 [D. Kühn and D. Osthus, Combinatorica, 29 (2009), pp. 65-107] which resolves this problem, up to an additive constant, for all graphs F. In this paper 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. [ABSTRACT FROM AUTHOR]