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

摘要

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