On Multi-Colourings of Cubic Graphs, and Conjectures of Fulkerson and Tutte
Paul D. Seymour · Proceedings of the London Mathematical Society · 1979
It is well known that the Petersen graph is not 3-edge-colourable; that is, if we regard its 1-factors as (0, l)-functions on the set of edges, the constant function 1 cannot be obtained by adding some of them together. In fact, 1 cannot be obtained even if we permit subtraction as well. Here