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Nesting partial Steiner triple systems with 2-regular leave graphs

✍ Scribed by K.T. Phelps; C.A. Rodger

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 505 KB
Volume: 112
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)90231-h

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✦ Synopsis

Phelps, K.T. and C.A. Rodger, Nesting partial Steiner triple systems with 2-regular leave graphs, Discrete Mathematics 112 (1993) 1655172.

In this paper we consider the problem of nesting partial Steiner triple systems. Among other results, we show that if there exists a nesting of a partial Steiner triple system of order 3p in which the leave graph consists of 3 vertex disjoint cycles of length p, then for any 2-factor H with 6x + 3 > 21p vertices in which all cycles have length divisible by p, there exists a nesting of a partial Steiner triple system with leave graph H.