Note on Factorization of Complete Graphs into Caterpillars with Small Diameters

Abstract

We prove in this note that certain caterpillars with diameter 4 or 5 do not factorize complete graphs. This together with results by Kovarova [2,3] and Kubesa [5] gives the complete characterization of the caterpillars with diameter 4 that factorize the complete graph $K_{2n}$. For diameter 5, we again complement results by Kovarova [4] and Kubesa [6-9] to give the complete characterization for certain class of caterpillars.