Article ID Journal Published Year Pages File Type
4649391 Discrete Mathematics 2010 5 Pages PDF
Abstract

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)(2k−2)-strong semicomplete digraphs which contain no spanning kk-strong tournament and conjecture that every(2k−1)(2k−1)-strong semicomplete digraph which is not the complete digraph K2k∗ on 2k2k vertices contains a spanning kk-strong tournament.

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics
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