A one-to-two disjoint-path cover of a graph G is a pair (P1, P2) of two vertex-disjoint paths that connect one source to two sinks in G and span G. It is called ε-balanced if |ℓ(P1)−ℓ(P2)|=ε, where ℓ(P1) and ℓ(P2) denote the lengths of paths P1 and P2, respectively. The matching composition network is a family of interconnection networks, each of which connects two components with the same number of vertices by a perfect matching. This paper addresses some properties about one-to-two disjoint-path covers of matching composition networks. Applying the proposed main theorem, a one-to-two ε-balanced disjoint-path cover in some well-known interconnection networks, such as crossed cubes, twisted cubes, locally twisted cubes, etc., can be easily obtained for a given odd integer ε.
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
Tel.: +1 703 830 6300
Fax: +1 703 830 2300 firstname.lastname@example.org
(Corporate matters and books only) IOS Press c/o Accucoms US, Inc.
For North America Sales and Customer Service
West Point Commons
Lansdale PA 19446
Tel.: +1 866 855 8967
Fax: +1 215 660 5042 email@example.com