4 problems

Let $G$ be a planar bicoloured PBDTP graph, and let its edges carry the geometric signature. Form the associated sign matrix by assigning the corresponding geometric-signature sign…

Let $\mathcal G$ be a graph in the broader class considered by the cited work, with edge set $\mathcal E$, and let $\sigma:\mathcal E\mapsto\{\pm1\}$ be a signature. For every fini…

Let $\mathcal G$ be a planar bicolored graph in the more general class considered by the cited work, and let a geometric signature assign values in $\{0,1\}$ to the edges. A Kastel…

Let $\mathcal G$ be a planar non-bipartite graph embedded in the disk, and let $\sigma$ be a signature on its edges satisfying, for every finite face $\Omega$, the relation … where…