Circular Chromatic Index of Snarks
Ján Mazák · 2007
A circular r-edge-coloring of a graph G is a mapping c: E(G) → [0, r) such that for any two adjacent edges e and f of G we have 1 ≤ |c(e) − c(f) | ≤ r − 1. The circular chromatic index χ ′ c (G) is the infimum of all real numbers r such that G has a circular r-edge-coloring. We establish a general lower bound for the circular chromatic index of a snark G depending only on the order of G. This bound is asymptotically tight. We also determine the exact value of the circular chromatic index of the generalized Blanuˇsa snarks. In this case, the index takes infinitely many values and can be arbitrarily close to 3. The generalized Blanuˇsa snarks are the first explicit class of snarks with this