Labeling the Complete Bipartite Graph with No Zero Cycles
summary
Assign nonzero labels from an abelian group to edges of the complete bipartite graph K_{n,n} so that no cycle sums to zero; focus on characterizing which groups and labelings avoid zero-sum cycles. Uses combinatorial and algebraic techniques (abelian group properties, cycle-sum constraints) to construct or rule out such labelings and analyze their existence.
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