Lower bounds on the obstacle number of graphs

Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices of G are joined by an edge if and only if the corresponding points can be connected by a segment which avoids all obstacles. The obstacle number of G is the minimum number of obstacles in an obstacle representation of G. It is shown that there are graphs on n vertices with obstacle number at least Ω(n/logn).

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Padmini Mukkamala, János Pach, Dömötör Pálvölgyi
• Keywords: CORR 2011, Corresponding Points, Education, Obstacle Number, Obstacle Representation