2-Colourings in S(t, t + 1, v)

✍ Scribed by Mario Gionfriddo; Giovanni Lo Faro

• Book ID: 103056922
• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 305 KB
• Volume: 111
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(93)90161-l

✦ Synopsis

Let S(t, k, c) be any nontrivial Steiner system. In this paper we prove the nonexistence of 2colourings in Steiner systems S(t, t + 1, ~1) when t + 1 is an odd number. Further, we prove that if t + 1 is an even number and C is a blocking set of the system S(t, t + 1, L') then ICI =n/2.

Very little is known today about the existence of blocking sets in Steiner systems. Results on blocking sets in Steiner quadruple systems have been obtained by Doyen