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Quasi-residual 2-designs, \(1\tfrac{1}{2}\)-designs, and strongly regular multigraphs

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Abstract

It is proved that a quasi-residual 2-(v, k, λ)-design with k>1/2λ5+O(λ4) can be embedded into a symmetric 2-design. This improves a result by Bose, Shrikhande, and Singhi [1]. Our proof uses properties of strongly regular multigraphs and \(1\tfrac{1}{2}\)-designs. In particular, we give a simple sufficient condition for a strongly regular multigraph to be isomorphic to the block multigraph of a 2-design.

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Bibliography

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Authors and Affiliations

  1. Institut für angewandte Mathematik, Universität Freiburg, Hermann Herder-Strasse 10, 7800, Freiburg i Br., W. Germany

    Arnold Neumaier

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  1. Arnold Neumaier
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Part of this research was done while the author was at Westfield College, London.

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Neumaier, A. Quasi-residual 2-designs, \(1\tfrac{1}{2}\)-designs, and strongly regular multigraphs. Geom Dedicata 12, 351–366 (1982). https://doi.org/10.1007/BF00147577

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  • DOI: https://doi.org/10.1007/BF00147577

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