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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
##### Keywords:
connectivity of digraphs; semicomplete digraph; tournament
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##### References:
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