8 problems

Blue-polygon bichromatic-face conjecture. Given a blue $k$-gon $P$ with at least $k-4$ red pseudolines passing through, there exists a bichromatic triangle or quadrangle on its ins…

Triangle-pseudoline incidence graph conjecture. The triangle-pseudoline incidence graph of a pseudoline arrangement is connected.

Björner–Las Vergnas–Sturmfels–White–Ziegler conjecture. Every bicolored arrangement has a bichromatic triangle.

Let $\mathcal{L}\subset\mathbb{RP}^2$ be an essential pseudoline arrangement, and let $M$ be its matroid. Let $Q$ be the Hirzebruch quadratic form of $M$, and let the semistable co…

Let $\mathcal{A}$ be an arrangement of pseudolines, and let $\operatorname{mx}(\mathcal{A})$ denote the maximum number of crossings on any pseudoline. A coloring of the crossings i…

For a finite set of points in the plane, consider every line determined by at least two points of the set, and compare the numbers of points on its two sides. Stretchable-configura…

Stretchability conjecture. Every simplicial arrangement with at most $14$ pseudolines is stretchable.

Grünbaum's conjecture. Up to isomorphism, there are only $5$ simplicial unstretchable arrangements of $15$ or $16$ pseudolines.