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A well-quasi-order for tournaments. (English) Zbl 1221.05178
Summary: A digraph \(H\) is immersed in a digraph \(G\) if the vertices of \(H\) are mapped to (distinct) vertices of \(G\), and the edges of \(H\) are mapped to directed paths joining the corresponding pairs of vertices of \(G\), in such a way that the paths are pairwise edge-disjoint. For graphs the same relation (using paths instead of directed paths) is a well-quasi-order; that is, in every infinite set of graphs some one of them is immersed in some other. The same is not true for digraphs in general; but we show it is true for tournaments (a tournament is a directed complete graph).

MSC:
05C20 Directed graphs (digraphs), tournaments
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