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.
The Doyen-Wilson theorem for 3-sun systems
Lo Faro, Giovanni
;Tripodi, Antoinette
2019-01-01
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.File in questo prodotto:
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