Nowhere-Zero Flows on Signed Complete and Complete Bipartite Graphs
Edita Máčajová, Edita Rollová · Journal of Graph Theory · 2014
Bouchet's conjecture asserts that each signed graph which admits a nowhere-zero flow has a nowhere-zero 6-flow. We verify this conjecture for two basic classes of signed graphs—signed complete and signed complete bipartite graphs by proving that each such flow-admissible graph admits a nowhere-zero 4-flow and we characterise those which have a nowhere-zero 2-flow and a nowhere-zero 3-flow.