Designs with mutually orthogonal resolutions and decompositions of edge-colored graphs

✍ Scribed by E. R. Lamken

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 298 KB
• Volume: 17
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20225

✦ Synopsis

Abstract

Two resolutions R and R^′^ of a combinatorial design are called orthogonal if |R~i~∩R|≤1 for all R~i~∈R and R∈R^′^. A set Q={R^1^, R^2^, …, R^d^} of d resolutions of a combinatorial design is called a set of mutually orthogonal resolutions (MORs) if the resolutions of Q are pairwise orthogonal. In this paper, we establish necessary and sufficient conditions for the asymptotic existence of a (v, k, 1)‐BIBD with d mutually orthogonal resolutions for d≥2 and k≥3 and necessary and sufficient conditions for the asymptotic existence of a (v, k, k−1)‐BIBD with d mutually orthogonal near resolutions for d≥2 and k≥3. We use complementary designs and the most general form of an asymptotic existence theorem for decompositions of edge‐colored complete digraphs into prespecified edge‐colored subgraphs. © 2009 Wiley Periodicals, Inc. J Combin Designs 17: 425–447, 2009