The following new results concerning 1-factorizations of the complete graph are proved: (1) There are exactly 6 equivalence classes of 1-factorizations of the complete graph with 8 vertices. (2). There are exactly 396 equivalence classes of 1-factorizations of the complete graph with 10 vertices. Representatives of each of the equivalence classes are presented. The size of the automorphism group of each equivalence class of 1-factorizations of the complete graph with 2n vertices for n ≤ 5 is also found.
Several theorems and results related to 1-factorizations of the complete graph are presented, and the relationship to round robin schedules is shown. An application problem demonstrates the importance of the choice of the equivalence class of round robin schedules in the solvability of the problem. / Graduate
|Date||10 June 2016|
|Creators||Gelling, Eric Neil|
|Contributors||Odeh, Robert E.|
|Source Sets||University of Victoria|
|Rights||Available to the World Wide Web, http://creativecommons.org/licenses/by-nc-nd/2.5/ca/|
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