A Steiner triple system which colours all cubic graphs

Grannell, Mike; Griggs, Terry; Knor, Martin and Skoviera, Martin (2004). A Steiner triple system which colours all cubic graphs. Journal of Graph Theory, 46(1) pp. 15–24.

DOI: https://doi.org/10.1002/jgt.10166


We prove that there is a Steiner triple system such that every simple cubic graph can have its edges colored by points of in such a way that for each vertex the colors of the three incident edges form a triple in . This result complements the result of Holroyd and koviera 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.

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