Triangle-Free Planar Graphs as Segment Intersection Graphs
Natalia de Castro, Francisco Javier Cobos, Juan Carlos Dana, Alberto Márquez, Marc Noy · WORLD SCIENTIFIC eBooks · 2004
Abstract. 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. 1