The Petersen graph is not 3-edge-colorable--a new proof

We give a new proof that the Petersen graph is not 3-edge-colorable. J. Petersen introduced the most well known graph, the Petersen graph, as an example of a cubic bridgeless graph that is not Tait colorable, i.e. it is not 3-edge-colorable. It is easy to see the equivalence between the following statements, but most proofs for each of them use a case by case argument [1]. Theorem 1 For the Petersen graph P the following are equivalent: (1) P is not 3-edge-colorable; (2) P is not Hamiltonian; (3) P does not admit a nowhere-zero 4-flow. Here we give a new proof of: Proposition 2 The Petersen graph is not 3-edge-colorable. ∗Supported in part by the Ministry of Science and Technology of Slovenia, Research Project Z1-3129 and by a postdoctoral fellowship of PIMS.