5 problems

Let $G$ be a 4-connected planar triangulation. A contact representation by homothetic triangles represents the vertices of $G$ by homothetic triangles whose prescribed contacts cor…

Rectangular-flat-torus grid contact conjecture. Every bipartite toroidal graph without loops has a grid contact representation on the rectangular flat torus.

Rectangular-flat-torus tessellation conjecture. Every toroidal graph without loops has a tessellation representation on the rectangular flat torus.

Termination conjecture. The algorithm terminates with a non-negative solution for every graph $G$ which is an inner triangulation of a $5$-gon, and for every initial five color for…

Gonçalves–Lévêque–Pinlou conjecture. Every 3-connected planar graph admits such a primal-dual contact representation by right triangles.