Infinite grids in digraphs
Abstract
Halin proved that every graph with an end ω containing infinitely many pairwise disjoint rays admits a subdivision of the infinite quarter-grid as a subgraph where all rays from that subgraph belong to ω. We will prove a corresponding statement for digraphs, that is, we will prove that every digraph that has an end with infinitely many pairwise disjoint directed rays contains a subdivision of a grid-like digraph all of whose directed rays belong to that end.
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