Circular Chromatic Index of Generalized Blanuša Snarks

Circular Chromatic Index of Generalized Blanusa Snarks

In his Master’s thesis, Ján Mazák proved that the circular chromatic index of the type 1 generalized Blanuša snark B n equals 3+ 2 n . This result provided the first infinite set of values of the circular chromatic index of snarks. In this paper we show the type 2 generalized Blanuša snark B n has circular chromatic index 3 + 1 b1+3n/2c . In particular, this proves that all numbers 3 + 1/n with...

The Circular Chromatic Index of Flower Snarks

We determine the circular chromatic index of flower snarks, by showing that χc(F3) = 7/2, χ ′ c(F5) = 17/5 and χ ′ c(Fk) = 10/3 for every odd integer k ≥ 7, where Fk denotes the flower snark on 4k vertices.

The circular chromatic index of Goldberg snarks

We determine the exact values of the circular chromatic index of the Goldberg snarks, and of a related family, the twisted Goldberg snarks.

Asymptotic Lower Bounds on Circular Chromatic Index of Snarks

We prove that the circular chromatic index of a cubic graph G with 2k vertices and chromatic index 4 is at least 3 + 2/k. This bound is (asymptotically) optimal for an infinite class of cubic graphs containing bridges. We also show that the constant 2 in the above bound can be increased for graphs with larger girth or higher connectivity. In particular, if G has girth at least 5, its circular c...

The circular chromatic index