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Spanning 2-strong tournaments in 3-strong semicomplete digraphs. (English) Zbl 1221.05172
Summary: We prove that every 3-strong semicomplete digraph on at least 5 vertices contains a spanning 2-strong tournament. Our proof is constructive and implies a polynomial algorithm for finding a spanning 2-strong tournament in a given 3-strong semicomplete digraph. We also show that there are infinitely many (\(2k - 2\))-strong semicomplete digraphs which contain no spanning \(k\)-strong tournament and conjecture that every\((2k - 1)\)-strong semicomplete digraph which is not the complete digraph \(K^{\ast }_{2k}\) on \(2k\) vertices contains a spanning \(k\)-strong tournament.

MSC:
05C20 Directed graphs (digraphs), tournaments
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