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Maximal arcs in Steiner systems S(2,4,v)
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Maximal arcs in Steiner systems S(2,4,v)

Abstract

A maximal arc in a Steiner system S(2,4,v) is a set of elements which intersects every block in either two or zero elements. It is well known that v≡4(mod12) is a necessary condition for an S(2,4,v) to possess a maximal arc. We describe methods of constructing an S(2,4,v) with a maximal arc, and settle the longstanding sufficiency question in a strong way. We show that for any v≡4(mod12), we can construct a resolvable S(2,4,v) containing a triple of maximal arcs, all mutually intersecting in a common point. An application to the motivating colouring problem is presented.

Authors

Greig M; Rosa A

Volume

267

Pagination

pp. 143-151

Publisher

Elsevier

Publication Date

June 6, 2003

DOI

10.1016/s0012-365x(02)00609-x

Conference proceedings

Discrete Mathematics

Issue

1-3

ISSN

0012-365X

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