NZ-flows in strong products of graphs

: We prove that the strong product G1 G2 of G1 and G2 is Z3-flow contractible if and only if G1 G2 is not T K2, where T is a tree (we call T K2 a K4-tree). It follows that G1 G2 admits an NZ 3-flow unless G1 G2 is a K4-tree. We also give a constructive proof that yields a polynomial algorithm whose output is an NZ 3-flow if G1 G2 is not a K4-tree, and an NZ 4-flow otherwise. ᭧ 2009 Wiley Periodicals, Inc. J Graph Theory 64: 267–276, 2010 MSC: 05C15; 05C75; 05C38

• Type: Journal
• Year: 2010
• Where: JGT
• Authors: Wilfried Imrich, Iztok Peterin, Simon Spacapan, Cun-Quan Zhang
• Keywords: JGT 2010, Strong Product, Wiley Periodicals, Z3-flow Contractible