Journal
GRAPHS AND COMBINATORICS
Volume 33, Issue 2, Pages 321-333Publisher
SPRINGER JAPAN KK
DOI: 10.1007/s00373-017-1766-7
Keywords
Spanning tree; 1-factorization; Complete graph; Matching
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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.
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