# surface

## 5-local-tensions ★★

Author(s): DeVos

Conjecture   There exists a fixed constant (probably suffices) so that every embedded (loopless) graph with edge-width has a 5-local-tension.

Keywords: coloring; surface; tension

## Drawing disconnected graphs on surfaces ★★

Author(s): DeVos; Mohar; Samal

Conjecture   Let be the disjoint union of the graphs and and let be a surface. Is it true that every optimal drawing of on has the property that and are disjoint?

Keywords: crossing number; surface

## Grunbaum's Conjecture ★★★

Author(s): Grunbaum

Conjecture   If is a simple loopless triangulation of an orientable surface, then the dual of is 3-edge-colorable.

Keywords: coloring; surface

## Consecutive non-orientable embedding obstructions ★★★

Author(s):

Conjecture   Is there a graph that is a minor-minimal obstruction for two non-orientable surfaces?

Keywords: minor; surface