Wilson-Schreiber Colourings of Cubic Graphs

An S-colouring of a cubic graph G is an edge-colouring of G by points of a Steiner triple system S such that the colours of any three edges meeting at a vertex form a block of S. In this note we present an infinite family of point-intransitive Steiner triple systems S such that (1) every simple cubic graph is S-colourable and (2) no proper subsystem of S has the same property. Only one point-intransitive system satisfying (1) and (2) was previously known.