How to build the factor-critical partial Steiner triple system of your dreams

Jack Neubecker (The University of Queensland)

A partial Steiner triple system \((V,B)\) consists of a set \(V\) of points and a collection \(B\) of \(3\)-element subsets (called triples) of \(V\) such that any two distinct points occur together in at most one triple. We say a partial Steiner triple system \((V,B)\) is factor critical if for all \(x in V\), there exists a set of mutually disjoint triples which covers every point except \(x\). We will illustrate various techniques for constructing factor-critical partial Steiner triple systems, and discuss their distinct merits in contributing to an existence theorem.

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