# An Update on the Existence of Kirkman Triple Systems with Subdesigns

@inproceedings{Dukes2021AnUO, title={An Update on the Existence of Kirkman Triple Systems with Subdesigns}, author={Peter J. Dukes and Esther R. Lamken}, year={2021} }

A Kirkman triple system of order v, KTS(v), is a resolvable Steiner triple system on v elements. In this paper, we investigate an open problem posed by Doug Stinson, namely the existence of KTS(v) which contain as a subdesign a Steiner triple system of order u, an STS(u). We present several different constructions for designs of this form. As a consequence, we completely settle the extremal case v = 2u+ 1, for which a list of possible exceptions had remained for close to 30 years. Our new…

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