# Grunbaum, Branko

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

Author(s): Grunbaum; Nash-Williams

\begin{conjecture} Every 4-connected toroidal graph has a Hamilton cycle. \end{conjecture}

Keywords:

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

Author(s): Grunbaum

\begin{problem} Do there exist 4-regular 4-chromatic graphs of arbitrarily high girth? \end{problem}

## Grunbaum's Conjecture ★★★

Author(s): Grunbaum

\begin{conjecture} If $G$ is a simple loopless \Def[triangulation]{triangulation (topology)} of an \Def{orientable surface}, then the dual of $G$ is 3-edge-colorable. \end{conjecture}