Cycle systems in the complete bipartite graph minus a one-factor
نویسندگان
چکیده
منابع مشابه
Cycle systems in the complete bipartite graph minus a one-factor
Let Kn,n − I denote the complete bipartite graph with n vertices in each part from which a 1-factor I has been removed. An m-cycle system of Kn,n − I is a collection of m-cycles whose edges partition Kn,n−I . Necessary conditions for the existence of such an m-cycle system are that m ≥ 4 is even, n ≥ 3 is odd, m ≤ 2n, and m | n(n − 1). In this paper, we show these necessary conditions are suffi...
متن کاملTitle 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).
متن کاملCycle 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 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).
متن کاملCyclic hamiltonian cycle systems of the complete graph minus a 1-factor
In this paper, we prove that cyclic hamiltonian cycle systems of the complete graph minus a 1-factor, Kn − I, exist if and only if n ≡ 2, 4( mod 8) and n 6= 2p with p prime and α ≥ 1.
متن کاملCyclic m-cycle systems of complete graphs minus a 1-factor
In this paper, we provide necessary and sufficient conditions for the existence of a cyclic m-cycle system of Kn − I when m and n are even and m | n.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2004
ISSN: 0012-365X
DOI: 10.1016/j.disc.2003.11.021