Non-bicritical Critical Snarks

Abstract

Snarks are cubic graphs with chromatic index Ø 0 = 4. A snark G is called critical if Ø 0 (G \Gamma fv; wg) = 3 for any two adjacent vertices v and w, and it is called bicritical if Ø 0 (G \Gamma fv; wg) = 3 for any two vertices v and w. We construct infinite families of critical snarks which are not bicritical. This solves a problem stated by Nedela and Skoviera in [7]