2016/11/28 by Asahi Takaoka, Takaoka, Asahi · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #cs.DM #graph theory and CDMA systems #math.CO
paper · pdf · doi:10.48550/arxiv.1611.09003
6 pages, 14 figures, Keywords: Alternatly orientable graphs, Linear-interval orders, PI graphs, PI orders, Simple-triangle graphs, Vertex ordering characterization
arxiv created 2016/11/28 · openalex publication_date 2016/11/28 · arxiv updated 2016/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.