The Doyen-Wilson theorem for 3-sun systems

Authors

  • Giovanni Lo Faro University of Messina, Italy
  • Antoinette Tripodi University of Messina, Italy

DOI:

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

Keywords:

3-sun system, embedding, difference set

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.

Published

2018-09-20

Issue

Section

Articles