Contact and intersection representations

Abstract

A necessary and sufficient condition is given for a connected bipartite graph to be the incidence graph of a family of segments and points. We deduce that any 4-connected 3-colorable plane graph is the contact graph of a family of segments and that any 4-colored planar graph without an induced C4 using 4 colors is the intersection graph of a family of straight line segments. © Springer-Verlag Berlin Heidelberg 2004.