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Embedding 1-Factorizations of K n in PG(2, 32)

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Abstract

1-Factorizations of the complete graph K n embedded in a finite Desarguesian projective plane PG(2, q), q even, are hyperfocused arcs of size n. The classification of hyperfocused arcs is motivated by applications to 2-level secret sharing schemes. So far it has been done for q  ≤ 16, and for special types of hyperfocused arcs. In this paper the case q = 32 is investigated and the following two results are proven. (i) Uniqueness of hyperfocused 12-arcs, up to projectivities. (ii) Non-existence of hyperfocused 14-arcs.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, via Vanvitelli 1, 06123, Perugia, Italy

    Giorgio Faina, Cristiano Parrettini & Fabio Pasticci

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  1. Giorgio Faina
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  2. Cristiano Parrettini
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  3. Fabio Pasticci
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Correspondence to Giorgio Faina.

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Faina, G., Parrettini, C. & Pasticci, F. Embedding 1-Factorizations of K n in PG(2, 32). Graphs and Combinatorics 29, 883–892 (2013). https://doi.org/10.1007/s00373-012-1166-y

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  • DOI: https://doi.org/10.1007/s00373-012-1166-y

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