A Theorem on Integer Flows on Cartesian Products of Graphs Wilfried Imrich 1 * and Riste S ˇ krekovski 2 1 DEPARTMENT OF APPLIED MATHEMATICS MONTANUNIVERSITA ¨ T LEOBEN FRANZ-JOSEF STRAE 18 A-8700 LEOBEN, AUSTRIA E-mail: imrich@unileoben.ac.at 2 DEPARTMENT OF MATHEMATICS UNIVERSITY OF LJUBLJANA JADRANSKA 19 1111 LJUBLJANA, SLOVENIA Received July 16, 2001; Revised November 16, 2002 DOI 10.1002/jgt.10100 Abstract: It is shown that the Cartesian product of two nontrivial connected graphs admits a nowhere-zero 4-flow. If both factors are bip- artite, then the product admits a nowhere-zero 3-flow. ß 2003 Wiley Periodicals, Inc. J Graph Theory 43: 93–98, 2003 Keywords: Integer flows, Cartesian products —————————————————— Contract grant sponsors: Ministry of Science and Technology of Slovenia (W. I); Contract grant sponsor: Research Project ZI-3129 (W. I). *Correspondence to: Wilfried Imrich, Department of Applied Mathematics, Montanuniversita ¨ t Leober, Frang-Josefstrae 18, Leoben A-8700, Austria. E-mail: imrich@unileoben.ac.at ß 2003 Wiley Periodicals, Inc.