Triangle-Free Planar Graphs as Segments Intersection Graphs
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.
KeywordsPlanar Graph Intersection Graph Vertical Segment Outer Face Horizontal Segment
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