Obstacle numbers of graphs

23Citations
Citations of this article
8Readers
Mendeley users who have this article in their library.

This article is free to access.

Abstract

An obstacle representation of a graph G is a drawing of G in the plane with straight-line edges, together with a set of polygons (respectively, convex polygons) called obstacles, such that an edge exists in G if and only if it does not intersect an obstacle. The obstacle number (convex obstacle number) of G is the smallest number of obstacles (convex obstacles) in any obstacle representation of G. In this paper, we identify families of graphs with obstacle number 1 and construct graphs with arbitrarily large obstacle number (convex obstacle number). We prove that a graph has an obstacle representation with a single convex k-gon if and only if it is a circular arc graph with clique covering number at most k in which no two arcs cover the host circle. We also prove independently that a graph has an obstacle representation with a single segment obstacle if and only if it is the complement of an interval bigraph. © Springer Science+Business Media, LLC 2009.

Cite

CITATION STYLE

APA

Alpert, H., Koch, C., & Laison, J. D. (2010). Obstacle numbers of graphs. Discrete and Computational Geometry, 44(1), 223–244. https://doi.org/10.1007/s00454-009-9233-8

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free