IJPAM: Volume 26, No. 4 (2006)

ON THE EXISTENCE OF 3 AND 4-DESIGNS
IN COMPLETE GRAPHS

Marius Buliga
Department of Mathematics
University of Pittsburgh-Bradford
Bradford, PA 16701, USA
e-mail: buliga@pitt.edu


Abstract.It is shown how a select set of subgraphs of the complete graph on 13 vertices generate 3-designs when acted upon with a group of suitable transitivity properties. An argument for the non-existence of 4-designs generated by subgraphs of $K_n$ (for $1\leq n\leq 100$) is given in the last section.

Received: January 19, 2006

AMS Subject Classification: 05B05, 62K10

Key Words and Phrases: complete graph, automorphism group, degree, claw, triangle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 4