Math @ Duke

Publications [#235393] of Pankaj K. Agarwal
Papers Published
 Agarwal, PK; Alon, N; Aronov, B; Suri, S, Can visibility graphs Be represented compactly?,
Discrete & Computational Geometry, vol. 12 no. 1
(1994),
pp. 347365, ISSN 01795376 [doi]
(last updated on 2018/03/21)
Abstract: 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 wellknown 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 SpringerVerlag New York Inc.


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