Paper Info
Title
Nearly Kirkman triple systems of order 18 and Hanani triple systems of order 19
Abstract
A Hanani triple system of order 6n+1, HATS(6n+1), is a decomposition of the complete graph K\"6\"n\"+\"1 into 3n sets of 2n disjoint triangles and one set of n disjoint triangles. A nearly Kirkman triple system of order 6n, NKTS(6n), is a decomposition of K\"6\"n-F into 3n-1 sets of 2n disjoint triangles; here F is a one-factor of K\"6\"n. The Hanani triple systems of order 6n+1 and the nearly Kirkman triple systems of order 6n can be classified using the classification of the Steiner triple systems of order 6n+1. This is carried out here for n=3: There are 3787983639 isomorphism classes of HATS(19)s and 25328 isomorphism classes of NKTS(18)s. Several properties of the classified systems are tabulated. In particular, seven of the NKTS(18)s have orthogonal resolutions, and five of the HATS(19)s admit a pair of resolutions in which the almost parallel classes are orthogonal.
Year
DOI
Venue
2011
10.1016/j.disc.2011.02.005
Discrete Mathematics
Keywords
Field
DocType
steiner triple system,resolvable design,nearly kirkman triple system,hanani triple system,complete graph
Complete graph,Discrete mathematics,Monad (category theory),Combinatorics,Disjoint sets,Triple system,Isomorphism,Mathematics,Steiner system
Journal
Volume
Issue
ISSN
311
10-11
Discrete Mathematics
Citations 
PageRank 
References 
2
0.37
5
Authors
5
Name
Order
Citations
PageRank
Charles J. Colbourn12726290.04
Petteri Kaski291266.03
Patric R.J. Östergård3446.22
David A. Pike46714.70
Olli Pottonen5868.99