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|Abstract:||Given $k$ pairs of vertices $(s_i,t_i)$, $1\le i\le k$, of a digraph $G$, how can we test whether there exist $k$ vertex-disjoint directed paths from $s_i$ to $t_i$ for $1\le i\le k$? This is NP-complete in general digraphs, even for $k = 2$, but for $k=2$ there is a polynomial-time algorithm when $G$ is a tournament (or more generally, a semicomplete digraph), due to Bang-Jensen and Thomassen. Here we prove that for all fixed $k$ there is a polynomial-time algorithm to solve the problem when $G$ is semicomplete.|
|Electronic Publication Date:||1-Dec-2014|
|Citation:||M. Chudnovsky, A. Scott, amd P. Seymour, Disjoint paths in tournaments, Adv Math 270 (2015), 582–597.|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Advances in mathematics.|
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