Planar segment visibility graphs - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Computational Geometry Year : 2000

Planar segment visibility graphs

C.T. Hoang
  • Function : Author
K. Kilakos
  • Function : Author
M. Noy
  • Function : Author

Abstract

Given a set of n disjoint line segments in the plane, the segment visibility graph is the graph whose $2n$ vertices correspond to the endpoints of the line segments and whose edges connect every pair of vertices whose corresponding endpoints can see each other. In this paper we characterize and provide a polynomial time recognition algorithm for planar segment visibility graphs. Actually, we caracterize segment visibility graphs that do not contain the complete graph on 5 vertices as a minor, qnd show that this class is the same as the class of planar segment visibility graphs. We use and prove the fact that every segment visibility graph contains the complete graph on 4 vertices as a subgraph. In fact, we prove a stronger result: every set of n line segments determines at least n-3 empty convex quadrilaterals.
Not file

Dates and versions

inria-00099259 , version 1 (26-09-2006)

Identifiers

  • HAL Id : inria-00099259 , version 1

Cite

Hazel Everett, C.T. Hoang, K. Kilakos, M. Noy. Planar segment visibility graphs. Computational Geometry, 2000, 16 (4), pp.235-243. ⟨inria-00099259⟩
53 View
0 Download

Share

Gmail Facebook Twitter LinkedIn More