Contact and intersection representations

Authors:
Hubert de Fraysseix;Patrice Ossona de Mendez
Affiliations:
UMR 8557, CNRS, Paris, France;UMR 8557, CNRS, Paris, France
Venue:
GD'04 Proceedings of the 12th international conference on Graph Drawing
Year:
2004

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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.