Counterexamples to Jaeger's Circular Flow Conjecture

Abstract It was conjectured by Jaeger that every 4 p-edge-connected graph admits a modulo ( 2 p + 1 ) -orientation (and, therefore, admits a nowhere-zero circular ( 2 + 1 p ) -flow). This conjecture was partially proved by Lovasz et al. (2013) [7] for 6 p -edge-connected graphs. In this paper, infinite families of counterexamples to Jaeger's conjecture are presented. For p ≥ 3 , there are 4 p -edge-connected graphs not admitting modulo ( 2 p + 1 ) -orientation; for p ≥ 5 , there are ( 4 p + 1 ) -edge-connected graphs not admitting modulo ( 2 p + 1 ) -orientation.