Negative cycles in complete signed graphs Original Research Article

Using an inclusion-exclusion formula for the symmetric difference and its associated Bonferroni inequalities, some extremal and divisibility properties for the number of negative p-cycles of Kn are deduced. It is also shown that the asymptotic probability that a p-cycle of Kn is negative does not depend on the structure of the subgraph spanned by negative edges provided this subgraph has bounded degrees.