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 C 4 using 4 colors is the intersection graph of a family of straight line segments.
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de Fraysseix, H., Ossona de Mendez, P. (2005). Contact and Intersection Representations. In: Pach, J. (eds) Graph Drawing. GD 2004. Lecture Notes in Computer Science, vol 3383. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31843-9_23
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DOI: https://doi.org/10.1007/978-3-540-31843-9_23
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