Infinite families of Kochol superpositions of Goldberg with Blowup snarks are Type 2

Abstract

A q-total coloring of a graph G is an assignment of q colors to the vertices and edges of G, so that adjacent or incident elements have different colors. The Total Coloring Conjecture (TCC) asserts that an optimum total coloring of G has at least ∆+1 and at most ∆+2 colors. We determine that all members of new infinite families of snarks obtained by the Kochol superposition of Goldberg with Blowup snarks are Type 1.