Decompositions of Various Complete Graphs into Isomorphic Copies of 4-cycles with Three Pendant Edges

Abstract

An $H$-decomposition of a graph $G$ is a partition of the edges of $G$ into copies isomorphic to $H$. When the decomposition is not feasible, one looks for the best possible by minimizing: the number of unused edges (leave of a packing), or the number of reused edges (padding of a covering). We consider the $H$-decomposition, packing, and covering of the complete graphs and complete bipartite graphs, where $H$ is a 4-cycle with three pendant edges.