On some properties of the intersection graph of half-planes induced by a set of lines

• Main Authors: Sancho, Marco Angelo, Tan, Alvin T.
• Format: text
• Language: English
• Published: Animo Repository 2007
• Subjects: Graph theory
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/17475
• Institution: De La Salle University

This study presents some properties of the intersection graph of a finite set of half-planes induced by a set of lines. The results are divided into two parts. The first part, which appears in Chapter 3, gives some of the properties of the graph G(Ln). Most of the results presented here are original results by the researchers. The second part, which is contained in Chapter 4, is an exposition of the first two sections of the paper entitled "On the Intersection Graphs of Halfplanes and of Line Segments in the Plane" by Dr. Severino Gervacio. It includes a characterization for a graph to be the intersection graph of a set of half-planes using the notion of neighborhood-ordered graphs. The study also includes a program which implements the results of the paper by Dr. Gervacio. Given a user-input graph, the program determines if the graph can be represented as the intersection graph of a given set of half-planes and if so, it proceeds to generate such a set of half-planes.