Routing permutations in the hypercube

Olivier Baudon (1) , Guillaume Fertin (2) , Ivan Havel (3)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 LINA - Laboratoire d'Informatique de Nantes Atlantique
3 Mathematical Institute [Praha] - Academy of Sciences

We study an n-dimensional directed symmetric hypercube Hn, in which every pair of adjacent vertices is connected by two arcs of opposite directions. Using the computer, we show that for H4 and for any permutation on its vertices, there exists a system of pairwise arc-disjoint directed paths from each vertex to its target in the permutation.

Mots clés: hypercube; routing permutations; Szymanski's conjecture

Domaines: Mathématique discrète [cs.DM]

Olivier Baudon, Guillaume Fertin, Ivan Havel. Routing permutations in the hypercube. International Workshop on Graph-Theoretic Concepts in Computer Science WG'99, Jun 1999, Ascona, Switzerland. pp.179-190. ⟨hal-00649015⟩