On representations by contact and intersection of segments
De Fraysseix, Hubert and Ossona de Mendez, Patrice (2007) On representations by contact and intersection of segments. [Journal (Paginated)]
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A necessary and sufficient condition is given for a connected bipartite graph to be the incidence graph of a contact 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.
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