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Selected Papers from the 1999 Symposium on Graph Drawing
DOI: 10.7155/jgaa.00043
Triangle-Free Planar Graphs and Segment Intersection Graphs
Vol. 6, no. 1, pp. 7-26, 2002. Regular paper.
Abstract We prove that every triangle-free planar graph is the
intersection graph 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. This
particular class of intersection graphs is also known as
contact graphs.
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Submitted: October 1999.
Revised: February 2001.
Revised: July 2001.
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