# Grunbaum, Branko

## Every 4-connected toroidal graph has a Hamilton cycle ★★

Author(s): Grunbaum; Nash-Williams

**Conjecture**Every 4-connected toroidal graph has a Hamilton cycle.

Keywords:

## 4-regular 4-chromatic graphs of high girth ★★

Author(s): Grunbaum

**Problem**Do there exist 4-regular 4-chromatic graphs of arbitrarily high girth?

## 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.