Plane integral drawings of planar graphs Original Research Article

A plane integral drawing of a planar graph G is a realization of G in the plane such that the vertices of G are mapped into distinct points and the edges of G are mapped into straight-line segments of integer length which connect the corresponding vertices such that two edges have no inner point in common. We conjecture that plane integral drawings exist for all planar graphs, and we give parts of a proof of this conjecture.