Equipartite gregarious 6- and 8-cycle systems

Billington, Elizabeth J., Smith, Benjamin R. and Hoffman, D. G. (2007) Equipartite gregarious 6- and 8-cycle systems. Discrete Mathematics, 307 13: 1659-1667. doi:10.1016/j.disc.2006.09.016

Author Billington, Elizabeth J.
Smith, Benjamin R.
Hoffman, D. G.
Title Equipartite gregarious 6- and 8-cycle systems
Journal name Discrete Mathematics   Check publisher's open access policy
ISSN 0012-365X
Publication date 2007
Year available 2006
Sub-type Article (original research)
DOI 10.1016/j.disc.2006.09.016
Volume 307
Issue 13
Start page 1659
End page 1667
Total pages 9
Editor D. B. West
Place of publication Netherlands
Publisher Elsevier
Collection year 2008
Language eng
Subject 230101 Mathematical Logic, Set Theory, Lattices And Combinatorics
780101 Mathematical sciences
Formatted abstract
A k-cycle decomposition of a complete multipartite graph is said to be gregarious if each k-cycle in the decomposition has its vertices in k different partite sets. Equipartite gregarious 3-cycle systems are 3-GDDs, and necessary and sufficient conditions for their existence are known (see for instance the CRC Handbook of Combinatorial Designs, 1996, C.J. Colbourn, J.H. Dinitz (Eds.), Section III 1.3). The cases of equipartite and of almost equipartite 4-cycle systems were recently dealt with by Billington and Hoffman. Here, for both 6-cycles and for 8-cycles, we give necessary and sufficient conditions for existence of a gregarious cycle decomposition of the complete equipartite graph Kn(a) (with n parts, n⩾6 or n⩾8, of size a)
Q-Index Code C1
Additional Notes Available online 13 November 2006 and published in journal 2007.

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Created: Mon, 31 Mar 2008, 11:25:24 EST by Marie Grove on behalf of School of Mathematics & Physics