  Two criteria for planarity of a Feynman diagram upon its propagators
(momentum flows) are presented. Instructive Mathematica programs that solve the
problem and examples are provided. A simple geometric argument is used to show
that while one can planarize non-planar graphs by embedding them on
higher-genus surfaces (in the example it is a torus), there is still a problem
with defining appropriate dual variables since the corresponding faces of the
graph are absorbed by torus generators.
