Neighborhoods in Maximum Packings of 2Kn and Quadratic Leaves of Triple Systems
Article first published online: 16 SEP 2013
© 2013 Wiley Periodicals, Inc.
Journal of Combinatorial Designs
Volume 22, Issue 12, pages 514–524, December 2014
How to Cite
Chaffee, J. and Rodger, C. A. (2014), Neighborhoods in Maximum Packings of 2Kn and Quadratic Leaves of Triple Systems. J. Combin. Designs, 22: 514–524. doi: 10.1002/jcd.21374
- Issue published online: 10 OCT 2014
- Article first published online: 16 SEP 2013
- Manuscript Revised: 14 AUG 2013
- Manuscript Received: 30 APR 2013
- neighborhood graphs;
- graph decompositions;
- quadratic leaves;
- partial triple systems
In this paper, two related problems are completely solved, extending two classic results by Colbourn and Rosa. In any partial triple system of , the neighborhood of a vertex v is the subgraph induced by . For (mod 3) with , it is shown that for any 2-factor F on or vertices, there exists a maximum packing of with triples such that F is the neighborhood of some vertex if and only if , thus extending the corresponding result for the case where or 1 (mod 3) by Colbourn and Rosa. This result, along with the companion result of Colbourn and Rosa, leads to a complete characterization of quadratic leaves of λ-fold partial triple systems for all , thereby extending the solution where by Colbourn and Rosa.