Packing Paths in Steiner Triple Systems

Abstract

We prove that any Steiner triple system $\mathcal{S}$, with $n = v(\mathcal{S})$ sufficiently large, admits a packing by almost spanning paths that covers almost all edges. More formally, for any $\mu > 0$, we obtain a family of $(1-\mu)n/3$ pairwise edge-disjoint paths, with $(1-\mu)n$ vertices each, all contained in $\mathcal{S}$.