Circular flow number of generalized Blanuša snarks

Abstract

A circular flow on a graph is an assignment of directions and flow values from R to the edges so that for each vertex the sum of the flow values on exiting edges equals the sum of the flow values on entering edges. A circular nowhere-zeror-flow is a circular flow ϕ with flow values satisfying 1≤|ϕ(e)|≤r−1 for each edge e. The circular flow number of a graph G is the infimum of all reals r such that G has a circular nowhere-zero r-flow. We prove that the circular flow number of all generalized Blanuša snarks except for the Petersen graph is 4.5. We also bound the circular flow number of Goldberg snarks, both from above and from below.