Uniform (<i>C</i>_<i>k</i>, <i>P</i>_<i>k</i>+1)-Factorizations of <i>K</i>_<i>n</i> − <i>I</i> When <i>k</i> Is Even

Abstract

Let H be a connected subgraph of a graph G. An H-factor of G is a spanning subgraph of G whose components are isomorphic to H. Given a set H of mutually non-isomorphic graphs, a uniform H-factorization of G is a partition of the edges of G into H-factors for some H∈H. In this article, we give a complete solution to the existence problem for uniform (Ck,Pk+1)-factorizations of Kn−I in the case when k is even.

Keywords

• graph factorization
• complete graph
• block design