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arXiv · 1611.09003

A vertex ordering characterization of simple-triangle graphs

Asahi Takaoka
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Abstract

Consider two horizontal lines in the plane. A pair of a point on the top line and an interval on the bottom line defines a triangle between two lines. The intersection graph of such triangles is called a simple-triangle graph. This paper shows a vertex ordering characterization of simple-triangle graphs as follows: a graph is a simple-triangle graph if and only if there is a linear ordering of the vertices that contains both an alternating orientation of the graph and a transitive orientation of the complement of the graph.

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Asahi Takaoka. 2016-11-28. A vertex ordering characterization of simple-triangle graphs. https://arxiv.org/abs/1611.09003

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