A Steiner triple system which colors all cubic graphs
M. J. Grannell, Terry S. Griggs, Martin Knor, Martin Škoviera · Journal of Graph Theory · 2004
Abstract We prove that there is a Steiner triple system 𝒯 such that every simple cubic graph can have its edges colored by points of 𝒯 in such a way that for each vertex the colors of the three incident edges form a triple in 𝒯. This result complements the result of Holroyd and Škoviera that every bridgeless cubic graph admits a similar coloring by any Steiner triple system of order greater than 3. The Steiner triple system employed in our proof has order 381 and is probably not the smallest possible. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 15–24, 2004