Small embeddings of partial directed cycle systems
نویسندگان
چکیده
منابع مشابه
Small embeddings for partial cycle systems of odd length
Let V(G) and E(G) denote the vertex and edge sets of a graph G respectively. Let Z, = (0, 1, . . . , n l}. Let K,, be the complete graph on n vertices. An m-cycle is a simple graph with m vertices, say uo, . . . , u,__~ in which the only edges are uou,_i and the edges joining ui to Ui+l (for 0 s i 6 m 2). We represent this cycle by (uo, . . . , u,_J or (uo, u,_~, u,_~, . . . , ul) or any cyclic...
متن کاملA small embedding for partial directed 6k-cycle systems
The main result in this paper is that for m == 0 (mod 6) a partial directed m-cycle system of order n can be embedded in a directed m-cycle system of order less than (mn)/2 + m/2 + 2m + 1. For fixed m, this bound is asymptotic in n to (mn) /2 which is approximately one-half of the best known bound of mn + (0 or 1).
متن کاملEmbedding partial bipartite directed cycle systems
A 2k-dicycle is a 2k-cycle of a directed bipartite graph and a 2k-dicycle system of order (m,n) is a triple (X, Y,D), where D is a collection of edge disjoint 2k-dicycles which partitions the edge set of the complete directed bipartite graph Dm,n with parts X and Y . A partial 2k-dicycle system of order (s, t) is a triple (S, T, P ), where P is a collection of edge disjoint 2k-dicycles of Ds,t ...
متن کاملSmall embeddings for partial triple systems of odd index
It has been conjectured that any partial triple system of order u and index λ can be embedded in a triple system of order v and index λ whenever v ≥ 2u + 1, λ(v − 1) is even and λ ( v 2 ) ≡ 0 (mod 3). This conjecture is known to hold for λ = 1 and for all even λ ≥ 2. Here the conjecture is proven for all remaining values of λ when u ≥ 28.
متن کاملA small embedding for large directed even cycle systems
A directed m-cycle system is a collection of directed edges of the form {(XbX2), (X2' X3)(X3, X4), ... , (Xm-l, xm), (xm' xd}, where Xl, X2, X3, ... , Xm are distinct. A partial directed m-cycle system of order n is a pair (8, C), where C is a collection of edge disjoint m-cycles of the complete directed graph Dn with vertex set S. If the cycles in C partition the edge set of Dn we have the def...
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: Bulletin of the Australian Mathematical Society
سال: 1992
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700011850