Circular chromatic index of generalized Blanuša snarks (Q1010755)

Summary: In his Master's thesis [``Circular chromatic index of snarks'', Comenius University Bratislava (2007)], Ján Mazák proved that the circular chromatic index of the type1 generalized Blanuša snark \(B^1_n\) equals \(3+\frac{2}{n}\). This result provided the first infinite set of values of the circular chromatic index of snarks. In this paper we show the type2 generalized Blanuša snark \(B^2_n\) has circular chromatic index \(3+{1/\lfloor{1+3n/2}\rfloor}\). In particular, this proves that all numbers \(3+1/n\) with \(n\geq 2\) are realized as the circular chromatic index of a snark. For \(n=1,2\) our proof is computer-assisted.