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Triangles in 2-factorizations

✍ Scribed by Dejter, I. J.; Franek, F.; Mendelsohn, E.; Rosa, A.

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 128 KB
Volume: 26
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199710)26:2<83::aid-jgt3>3.0.co;2-b

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✦ Synopsis

The triangle-spectrum for 2-factorizations of the complete graph K v is the set of all numbers δ such that there exists a 2-factorization of K v in which the total number of triangles equals δ. By applying mainly design-theoretic methods, we determine the triangle spectrum for all v ≡ 1 or 3 (mod 6), v ≥ 43, as well as for v = 7, 9, 13, 15, 21, and 27. For orders v = 19, 25, 31, 33, 37, 39, we leave only a total of 11 values undecided. To determine the triangle-spectrum for v ≡ 5 (mod 6) remains an open problem.

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