Factorizations of Complete Graphs into Spanning Trees with All Possible Maximum Degrees

Abstract

Fronček and Kovářová provided in [2] and [3]spanning trees of order 2n that factorize K _2n for every n ≥ 2 and for every feasible diameter d, 3 ≤ d ≤ 2n − 1. We extend their work and give a spanning tree on 2n vertices with a maximum degree ${\it \Delta}$ that factorize K _2n for every n ≥ 2 and for every feasible $2\leq {\it \Delta} \leq n$. We give a construction for both symmetric and non-symmetric spanning trees.

Research for this article was partially supported by the institutional project MSM6198910027.