Locally planar toroidal graphs are 5-colorable
Locally planar toroidal graphs are 5-colorable
If a graph can be embedded in a torus in such a way that all noncontractible cycles have length at least 8, then its vertices may be <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="5"> <mml:semantics> <mml:mn>5</mml:mn> <mml:annotation encoding="application/x-tex">5</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-colored. The conclusion remains true when some noncontractible cycles have length less …