TY - GEN

T1 - Can visibility graphs be represented compactly?

AU - Agarwal, Pankaj K.

AU - Alon, Noga

AU - Aronov, Boris

AU - Suri, Subhash

PY - 1993

Y1 - 1993

N2 - 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 = {G1, G2,..., Gk} is called a clique cover of G if (i) each Gi is a clique or a bipartite clique, and (ii) the union of Gi is G. The size of the clique cover G is defined as Σik=1 ni, where ni is the number of vertices in Gi. Our main result is that there exist visibility graphs of n nonintersecting line segments in the plane whose smallest clique cover has size Ω(n2/log2 n). An upper bound of O(n2/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 a size O(n log3 n), and that there are simple polygons whose visibility graphs require a clique cover of size Ω(n log n).

AB - 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 = {G1, G2,..., Gk} is called a clique cover of G if (i) each Gi is a clique or a bipartite clique, and (ii) the union of Gi is G. The size of the clique cover G is defined as Σik=1 ni, where ni is the number of vertices in Gi. Our main result is that there exist visibility graphs of n nonintersecting line segments in the plane whose smallest clique cover has size Ω(n2/log2 n). An upper bound of O(n2/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 a size O(n log3 n), and that there are simple polygons whose visibility graphs require a clique cover of size Ω(n log n).

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U2 - 10.1145/160985.161160

DO - 10.1145/160985.161160

M3 - Conference contribution

AN - SCOPUS:0027802232

SN - 0897915828

SN - 9780897915823

T3 - Proceedings of the 9th Annual Symposium on Computational Geometry

SP - 338

EP - 347

BT - Proceedings of the 9th Annual Symposium on Computational Geometry

PB - Publ by ACM

T2 - Proceedings of the 9th Annual Symposium on Computational Geometry

Y2 - 19 May 1993 through 21 May 1993

ER -