Jordán and Garamvölgyi's separator conjecture for globally linked pairs

Let G=G1G2G=G_1\cup G_2, where V(G1)V(G2)d+1|V(G_1)\cap V(G_2)|\leq d+1, and let u,vV(G1)V(G2)u,v\in V(G_1)\cap V(G_2). A pair is Rd\mathcal{R}_d-linked when it is contained in an Rd\mathcal{R}_d-circuit. Jordán and Garamvölgyi's separator conjecture. If {u,v}\{u,v\} is Rd\mathcal{R}_d-linked in both G1G_1 and G2G_2, then {u,v}\{u,v\} is globally linked in GG in Rd\mathbb{R}^d. The conjecture concerns how global linkage behaves under unions with small separators and remains unresolved in the source.

Sources & referencesView supporting material

Primary source

Dániel Garamvölgyi, “Stress-linked pairs of vertices and the generic stress matroid”, arXiv:2308.16851 (2025).

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