# Can visibility graphs Be represented compactly?

Published

Journal Article

We consider the problem of representing the visibility graph of line segments as a union of cliques and bipartite cliques. Given a graph G, a family G={G 1, G 2,..., G k } is called a clique cover of G if (i) each G i is a clique or a bipartite clique, and (ii) the union of G i is G. The size of the clique cover G is defined as ∑ i=1 k n i, where n i is the number of vertices in G i . Our main result is that there are visibility graphs of n nonintersecting line segments in the plane whose smallest clique cover has size Ω(n 2/log2 n). An upper bound of O(n 2/log n) on the clique cover follows from a well-known result in extremal graph theory. On the other hand, we show that the visibility graph of a simple polygon always admits a clique cover of size O(nlog3 n), and that there are simple polygons whose visibility graphs require a clique cover of size Ω(n log n). © 1994 Springer-Verlag New York Inc.

### Full Text

### Duke Authors

### Cited Authors

- Agarwal, PK; Alon, N; Aronov, B; Suri, S

### Published Date

- December 1, 1994

### Published In

### Volume / Issue

- 12 / 1

### Start / End Page

- 347 - 365

### Electronic International Standard Serial Number (EISSN)

- 1432-0444

### International Standard Serial Number (ISSN)

- 0179-5376

### Digital Object Identifier (DOI)

- 10.1007/BF02574385

### Citation Source

- Scopus