Spanning Tree Decompositions of Complete Graphs Orthogonal to Rotational 1-Factorizations (Article)

In Krussel et al. (ARS Comb 57:77–82, 2000), Krussel, Marshall, and Verall proved that whenever 2 n- 1 is a prime of the form 8 m+ 7 , there exists a spanning tree decomposition of K2 n orthogonal to the 1-factorization GK2 n. In this paper, we develop a technique for constructing spanning tree decompositions that are orthogonal to rotational 1-factorizations of K2 n. We apply our results to show that, for every n \u3e 2 , there exists a spanning tree decomposition orthogonal to GK2 n. We include similar applications to other rotational families of 1-factorizations, and provide directions for further research