A Separator Theorem for String Graphs and Its Applications
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
A separator theorem for string graphs and its applications
Combinatorics, Probability and Computing
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Let ${\cal C}$ be a family of n compact connected sets in the plane, whose intersection graph $G({\cal C})$ has no complete bipartite subgraph with k vertices in each of its classes. Then $G({\cal C})$ has at most n times a polylogarithmic number of edges, where the exponent of the logarithmic factor depends on k. In the case where ${\cal C}$ consists of convex sets, we improve this bound to O(n log n). If in addition k = 2, the bound can be further improved to O(n). © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 205–214, 2008