S. Fujita (Japan)

Transposition graph, routing, vertex-disjoint, matching.

A transposition graph is a Cayley graph in which vertices correspond to permutations and edges are placed between permutations that differ by exactly one transposition. In this paper, we propose an algorithm to ﬁnd a collection of vertex-disjoint paths connecting a given source vertex s and a given set of destination vertices D. The running time of the algorithm is polynomial to the number of des tination vertices, and the resultant path connecting s and each destination is longer than the length of a shortest path connecting those vertices by at most fourteen.

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