Grace Aspenson

Let K be any graph, and let G be a subgraph of K. If it is possible to partition the edges of K into disjoint replicas of G, then we say that K allows a G-decomposition. It is known that if a graph G with n edges admits a labeling that satisfies certain properties, then the complete graphs of orders 2nk and 2nk + 1 can be decomposed into disjoint copies of G for any integer k. I will be investigating the decomposition of complete graphs of orders 18k and 18k + 1 into unicyclic bipartite graphs with nine edges.