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.
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Máčajová et al. (2014) studied this question.
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