Triangle-Free Planar Graphs as Segments Intersection Graphs
De Castro, Natalia and Cobos, F. J. and Dana, J. C. and Márquez, Alberto and Noy, M. (1999) Triangle-Free Planar Graphs as Segments Intersection Graphs. In: Graph Drawing 7th International Symposium, GD’99, September 15-19, 1999, Štirín Castle, Czech Republic , pp. 341-350 (Official URL: http://dx.doi.org/10.1007/3-540-46648-7_35).
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We prove that every triangle-free planar graph is the graph of intersection of a set of segments in the plane. Moreover, the segments can be chosen in only three directions (horizontal, vertical and oblique) and in such a way that no two segments cross, i. e., intersect in a common interior point.
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