On decompositions of complete graphs into unicyclic disconnected bipartite graphs on nine edges - Alan Bonhert; Luke Branson; Patrick Joseph Otto (Electronic Journal of Graph Theory and Applications (EJGTA), 2023)
We use Rosa-type labelings to decompose complete graphs into unicyclic, disconnected, bipartite graphs on nine edges – namely, those featuring cyclic component C4, C6, or C8. For any such graph H, we prove there exists an H-design of K18k + 1 and K18k for all positive integers k.