English

The Doyen-Wilson theorem for 3-sun systems

Combinatorics 2017-05-02 v1

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.

Cite

@article{arxiv.1705.00040,
  title  = {The Doyen-Wilson theorem for 3-sun systems},
  author = {Giovanni Lo Faro and Antoinette Tripodi},
  journal= {arXiv preprint arXiv:1705.00040},
  year   = {2017}
}
R2 v1 2026-06-22T19:31:24.834Z