Doyen-Wilson Results for Odd Length Cycle Systems

Nesting of cycle systems of odd length

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...

The Doyen Wilson Theorem for Minimum Coverings with Triples

In this article necessary and sufficient conditions are found for aminimum covering ofKm with triples to be embedded in a minimum covering ofKn with triples. c © 1997 JohnWiley & Sons, Inc. J Combin Designs 5: 341–352, 1997

Two Doyen-Wilson theorems for maximum packings with triples

In this paper we complete the work begun by Mendelsohn and Rosa and by Hartman, finding necessary and sufficient conditions for a maximum packing with triples of order m MPT(m) to be embedded in an MPT(n). We also characterize when it is possible to embed an MPT(m) with leave LI in an MPT(n) with leave L2 in such a way that L1 C L2.

The Doyen-Wilson Theorem Extended to 5-Cycles

Let ~m = {0, 1 . . . . , m 1}. A n m-cycle is a graph (v0, V l , . . . , u~_ 1) with vertex set {viii ~ E m} and edge set {{vi, Vi+a}]i ~ 7/m} (reducing the subscript modulo m). A n m-cycle system of a graph G is an o rdered pair (V, C), where V is the vertex set of G and C is a set of m-cycles, the edges of which part i t ion the edges of G. A n m-cycle system (of order n) is an m-cycle system...