Ubiquitous configurations in Steiner triple systems

A Steiner triple system S is a C‐ubiquitous (where C is a configuration) if every line of S is contained in a copy of C, and is n‐ubiquitous if it is C‐ubiquitous for every n‐line configuration C. We determine the spectrum of 4‐ubiquitous Steiner triple systems as well as the spectra of C‐ubiquitous Steiner triple systems for all configurations C with five lines. © 1997 John Wiley & Sons, Inc.