Contact and Intersection Representations
De Fraysseix, Hubert and Ossona de Mendez, Patrice (2004) Contact and Intersection Representations. In: Graph Drawing 12th International Symposium, GD 2004, September 29-October 2, 2004, New York, NY, USA , pp. 217-227 (Official URL: http://dx.doi.org/10.1007/978-3-540-31843-9_23).
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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 C_4 using 4 colors is the intersection graph of a family of straight line segments.
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