Zaslavsky's edge-disjoint negative-cycle conjecture

From papers

Let Σ\Sigma be a signed graph. Denote by p(Σ)p^-(\Sigma) the maximum number of edge-disjoint negative cycles, by l(Σ)l(\Sigma) its frustration index, and by p(Σ)p(\Sigma) the maximum number of edge-disjoint cycles in its underlying graph. Zaslavsky's edge-disjoint negative-cycle conjecture. One always has

p(Σ)=min(l(Σ),p(Σ)).p^-(\Sigma)=\min\bigl(l(\Sigma),p(\Sigma)\bigr).

This asserts equality in both general bounds p(Σ)l(Σ)p^-(\Sigma)\leq l(\Sigma) and p(Σ)p(Σ)p^-(\Sigma)\leq p(\Sigma). The supplied text does not give evidence that the conjecture has been resolved, so its status is left open.

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Sources & referencesView supporting material

Primary source

Maximilien Gadouleau and Huiying Zeng, “On the maximum and negative frustration indices of graphs”, arXiv:2606.11108 (2026).

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