Graphes cubiques d'indice trois, graphes cubiques isochromatiques, graphes cubiques d'indice quatre

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The process introduced by E. Johnson [ Amer. Math. Monthly 73 (1966), 52–55] for constructing connected cubic graphs can be modified so as to obtain restricted classes of cubic graphs, in particular, those defined by their chromatic number or their chromatic index. We construct here the graphs of chromatic number three and the graphs whose chromatic number is equal to its chromatic index (isochromatic graphs). We then give results about the construction of the class of graphs of chromatic index four, and in particular, we construct an infinite class of “snarks.”