c ○ 2006 Society for Industrial and Applied Mathematics CYCLE DECOMPOSITIONS OF Kn,n − I ∗
نویسندگان
چکیده
Let Kn,n denote the complete bipartite graph with n vertices in each bipartition set and Kn,n − I denote Kn,n with a 1-factor removed. An m-cycle system of Kn,n − I is a collection T of m-cycles such that each edge of Kn,n − I is contained in a unique m-cycle of T . In this paper, it is proved that the necessary and sufficient conditions for the existence of an m-cycle system of Kn,n − I are n ≡ 1 (mod 2), m ≡ 0 (mod 2), 4 ≤ m ≤ 2n, and n(n− 1) ≡ 0 (mod m).
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تاریخ انتشار 2006