A set S of edge-disjoint hamilton cycles in a graph G is said to be maximal if the edges in the hamilton cycles in S induce a subgraph H of G such that G EÃ°HÃž contains no hamilton cycles. In thisâ€¦ (More)

The graph decomposition problem is well known. We say a subgraph G divides Km if the edges of Km can be partitioned into copies of G. Such a partition is called a G-decomposition or G-design. Theâ€¦ (More)

Let K (r) n be the order n uniform complete multigraph with edge multiplicity r. A spanning tree decomposition of K (r) n partitions its edge set into a family T of edge-induced spanning trees. In aâ€¦ (More)

We call T = (G1, G2, G3) a graph-triple of order t if the Gi are pairwise non-isomorphic graphs on t non-isolated vertices whose edges can be combined to form Kt. If m â‰¥ t, we say T divides Km ifâ€¦ (More)