Cycle Systems in the Complete Bipartite Graph Plus a One-Factor
نویسندگان
چکیده
Let Kn,n denote the complete bipartite graph with n vertices in each partite set and Kn,n+I denote Kn,n with a 1-factor added. It is proved in this paper that there exists an m-cycle system of Kn,n + I if and only if n ≡ 1 (mod 2), m ≡ 0 (mod 2), 4 ≤ m ≤ 2n and n(n + 1) ≡ 0 (mod m).
منابع مشابه
Title Cycle Systems in the Complete Bipartite Graph plus a One- Factor Cycle Systems in the Complete Bipartite Graph plus a One-factor *
Let Kn,n denote the complete bipartite graph with n vertices in each partite set and Kn,n+I denote Kn,n with a one-factor added. It is proved in this paper that there exists an m-cycle system of Kn,n + I if and only if n ≡ 1 (mod 2), m ≡ 0 (mod 2), 4 ≤ m ≤ 2n, and n(n + 1) ≡ 0 (mod m).
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عنوان ژورنال:
- SIAM J. Discrete Math.
دوره 21 شماره
صفحات -
تاریخ انتشار 2008