Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves

Bryant, D., Maenhaut, B., Quinn, K. and Webb, B. S. (2004) Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves. Discrete Mathematics, 284 1-3: 83-95. doi:10.1016/j.disc.2004.01.009


Author Bryant, D.
Maenhaut, B.
Quinn, K.
Webb, B. S.
Title Existence and embeddings of partial Steiner triple systems of order ten with cubic leaves
Journal name Discrete Mathematics   Check publisher's open access policy
ISSN 0012-365X
Publication date 2004-01-01
Sub-type Article (original research)
DOI 10.1016/j.disc.2004.01.009
Volume 284
Issue 1-3
Start page 83
End page 95
Total pages 13
Editor P. L. Hammer
Place of publication Netherlands
Publisher Elsevier BV
Language eng
Subject C1
230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Abstract Denote the set of 21 non-isomorphic cubic graphs of order 10 by L. We first determine precisely which L is an element of L occur as the leave of a partial Steiner triple system, thus settling the existence problem for partial Steiner triple systems of order 10 with cubic leaves. Then we settle the embedding problem for partial Steiner triple systems with leaves L is an element of L. This second result is obtained as a corollary of a more general result which gives, for each integer v greater than or equal to 10 and each L is an element of L, necessary and sufficient conditions for the existence of a partial Steiner triple system of order v with leave consisting of the complement of L and v - 10 isolated vertices. (C) 2004 Elsevier B.V. All rights reserved.
Keyword Mathematics
Steiner Triple System
Partial Steiner Triple System
Embedding
Q-Index Code C1

 
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Created: Wed, 15 Aug 2007, 12:59:18 EST