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

Autor:	Cristiano Parrettini, Giorgio Faina, Fabio Pasticci
Rok vydání:	2012
Předmět:	complete graphs Discrete mathematics hyperfocused arcs Complete graph 1-Factorizations complete graphs hyperfocused arcs Secret sharing Theoretical Computer Science Combinatorics 1-Factorizations Discrete Mathematics and Combinatorics Embedding Uniqueness Projective plane Mathematics
Zdroj:	Graphs and Combinatorics. 29:883-892
ISSN:	1435-5914 0911-0119
DOI:	10.1007/s00373-012-1166-y
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b23651b344a04b065880197583636512 https://doi.org/10.1007/s00373-012-1166-y Zobrazit plný text záznamu Full text from SpringerLink