The Doyen-Wilson theorem for 3-sun systems

Giovanni Lo Faro, Antoinette Tripodi

Abstract


A solution to the existence problem of G-designs with given subdesigns is known when G is a triangle with p = 0, 1, or 2 disjoint pendent edges: for p = 0, it is due to Doyen and Wilson, the first to pose such a problem for Steiner triple systems; for p = 1 and p = 2, the corresponding designs are kite systems and bull designs, respectively. Here, a complete solution to the problem is given in the remaining case where G is a 3-sun, i.e. a graph on six vertices consisting of a triangle with three pendent edges which form a 1-factor.


Keywords


3-sun system, embedding, difference set

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DOI: https://doi.org/10.26493/1855-3974.1490.eea

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications