Nowhere-zero flows in Cartesian bundles of graphs

We extend the results of Imrich and Škrekovski [J. Graph Theory 43 (2003) 93–98] concerning nowhere-zero flows in Cartesian product graphs to ‘twisted’ Cartesian products, that is, Cartesian bundles. Our main result states that every Cartesian bundle of two graphs without isolated vertices has a nowhere-zero 4-flow.