Directed cyclic Hamiltonian cycle systems of the complete symmetric digraph
نویسندگان
چکیده
منابع مشابه
Directed cyclic Hamiltonian cycle systems of the complete symmetric digraph
In this paper, we prove that directed cyclic hamiltonian cycle systems of the complete symmetric digraph, K∗ n, exist if and only if n ≡ 2 (mod 4) and n 6= 2p with p prime and α ≥ 1. We also show that directed cyclic hamiltonian cycle systems of the complete symmetric digraph minus a set of n/2 vertex-independent digons, (Kn− I)∗, exist if and only if n ≡ 0 (mod 4).
متن کاملCyclic Hamiltonian cycle systems of the complete graph
We prove that there exists a cyclic Hamiltonian k-cycle system of the complete graph if and only if k is odd but k = 15 and p with p prime and ¿ 1. As a consequence we have the existence of a cyclic k-cycle system of the complete graph on km vertices for any pair (k; m) of odd integers with k as above but (k; m) = (3; 3). c © 2003 Elsevier B.V. All rights reserved.
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 کاملThe Path-Cycle Symmetric Function of a Digraph
Recently, Stanley [21] has defined a symmetric function generalization of the chromatic polynomial of a graph. Independently, Chung and Graham [4] have defined a digraph polynomial called the cover polynomial which is closely related to the chromatic polynomial of a graph (in fact, as we shall see, the cover polynomial of a certain digraph associated to a poset P coincides with the chromatic po...
متن کاملExistence of cyclic k-cycle systems of the complete graph
Starting from earliest papers by Rosa we solve, directly and explicitly, the existence problem for cyclic k-cycle systems of the complete graph Kv with v ≡ 1 (mod 2k), and the existence problem for cyclic k-cycle systems of the complete m-partite graph Km×k with m and k being odd. As a particular consequence, a cyclic p-cycle system of Kv with p being a prime exists for all admissible values of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2008.01.016