NZ-flows in strong products of graphs

Wilfried Imrich, Iztok Peterin, Simon Špacapan, Cun-Quan Zhang
2009 Journal of Graph Theory  
We prove that the strong product G 1 G 2 of G 1 and G 2 is Z 3 -flow contractible if and only if G 1 G 2 is not T K 2 , where T is a tree (we call T K 2 a K 4 -tree). It follows that G 1 G 2 admits an NZ 3-flow unless G 1 G 2 is a K 4 -tree. We also give a constructive proof that yields a polynomial algorithm whose output is an NZ 3-flow if G 1 G 2 is not a K 4 -tree, and an NZ 4-flow otherwise. ᭧
doi:10.1002/jgt.20455 fatcat:5ozke4u52jdbnpqroa67bpettq