Star-Supermagic Decompositions of 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 کاملSymmetric Hamilton Cycle Decompositions of Complete Graphs Minus a 1-Factor
Let n ≥ 2 be an integer. The complete graph Kn with a 1-factor F removed has a decomposition into Hamilton cycles if and only if n is even. We show that Kn − F has a decomposition into Hamilton cycles which are symmetric with respect to the 1-factor F if and only if n ≡ 2, 4 mod 8. We also show that the complete bipartite graph Kn,n has a symmetric Hamilton cycle decomposition if and only if n ...
متن کاملCycle decompositions of the complete graph
For a positive integer n, let G be Kn if n is odd and Kn less a one-factor if n is even. In this paper it is shown that, for non-negative integers p, q and r, there is a decomposition of G into p 4-cycles, q 6-cycles and r 8-cycles if 4p+6q+8r = |E(G)|, q = 0 if n < 6 and r = 0 if n < 8.
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2017
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2017/5104701