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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
##### Keywords:
well-quasi-order; digraph; tournament; immersion; minor
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##### References:
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