Uniformly Resolvable Decompositions of <i>K_v</i>-<i>I</i> into <i>n</i>-Cycles and <i>n</i>-Stars, for Even <i>n</i>

Abstract

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. Given a set Γ of pairwise non-isomorphic graphs, a uniformly resolvable Γ-decomposition of a graph G is an edge decomposition of G into X-factors for some graph X∈Γ. In this article we completely solve the existence problem for decompositions of Kv-I into Cn-factors and K1,n-factors in the case when n is even.

Keywords

• graph decomposition
• factor
• uniform factorization