Factorizations of complete graphs into \([n,r,s,2]\)-caterpillars of diameter 5 with maximum end (Q2370391)

An \([n,r,s,2]\)-caterpillar of diameter 5 with maximum end is a tree on \(2n\) vertices that arises from the path \(P_6\) of length 5 by attaching \(n-2\) pendant edges to the neighbor of one of the endvertices of \(P_6\) and \(r-2\) and \(s-2\) pendant edges, respectively, to any two of the remaining vertices of \(P_6\) of degree two. A complete characterization of such caterpillars that factorize the complete graph \(K_{2n}\) is given.