Decompositions of Complete Graphs into Isomorphic Spanning Trees with Given Diameters

Abstract

We use a new technique for decomposition of complete graphs with even number of vertices based on $2n$-cyclic blended labeling to show that for every $k>1$ odd, and every $d$, $3\le d\le 2^{q}k–1$, there exists a spanning tree of diameter $d$ that factorizes $K_{2^{q}k}$.