4 problems

A signed graph $(G,\sigma)$ is a graph with a positive or negative sign on each edge. Its frustration index $l(G,\sigma)$ is the minimum number of negative edges among signatures s…

Facial-cycle conjecture. Every non-decomposable critically $k$-frustrated signed plane graph has exactly $2k$ facial cycles, each of which is a negative cycle.

Finiteness conjecture. For every positive integer $k$, the set $\mathcal{S}^*(k)$ is finite.

Finiteness conjecture. For every positive integer $k$, the set $\mathcal{L}^*(k)$ is finite.