Structural and Complexity Aspects of Line Systems of Graphs

We study line systems in metric spaces induced by graphs. A line is a subset of vertices defined by a relation of betweeness. We show that the class of all graphs having exactly k different lines is infinite if and only if it contains a graph with a bridge. We also study lines in random graphs--a random graph almost surely has `n 2

• Type: Journal
• Year: 2010
• Where: ISAAC
• Authors: Jozef Jirásek, Pavel Klavík
• Keywords: Algorithms, ISAAC 2010, Line Systems, Metric Space, Random Graph