26 research outputs found
On uniformly resolvable -designs
In this paper we consider the uniformly resolvable decompositions of the complete graph minus a 1-factor into subgraphs where each resolution class contains only blocks isomorphic to the same graph. We completely determine the spectrum for the case in which all the resolution classes consist of either 4-cycles or 3-stars
Uniformly resolvable decompositions of Kv in 1-factors and 4-stars
If X is a connected graph, then an X-factor of a larger graph is a spanning subgraph in which all of its components are isomorphic to X. A uniformly resolvable {X, Y }-decomposition of the complete graph Kv is an edge decomposition of Kv into exactly r X-factors and s Y -factors. In this article we determine necessary and sufficient conditions for when the complete graph Kv has a uniformly resolvable decompositions into 1-factors and K1,4-factors
α-Resolvable λ-fold G-designs
A λ-fold G-design is said to be α-resolvable if its blocks can be partitioned into classes such that every class contains each vertex exactly α times. In this paper we study the existence problem of an α-resolvable λ-fold G-design oforder v in the case when G is any connected subgraph of K_4 and prove that the necessary conditions for its existence are also sufficient
Decomposition of product graphs into sunlet graphs of order eight
For any integer , we define sunlet graph of order , denoted by , as the graph consisting of a cycle of length together with pendant vertices, each adjacent to exactly one vertex of the cycle. In this paper, we give necessary and sufficient conditions for the existence of -decomposition of tensor product and wreath product of complete graphs