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CPC
2010

A Separator Theorem for String Graphs and its Applications

9 years 9 months ago
A Separator Theorem for String Graphs and its Applications
A string graph is the intersection graph of a collection of continuous arcs in the plane. It is shown that any string graph with m edges can be separated into two parts of roughly equal size by the removal of O(m3/4 log m) vertices. This result is then used to deduce that every string graph with n vertices and no complete bipartite subgraph Kt,t has at most ctn edges, where ct is a constant depending only on t. Another application shows that locally tree-like string graphs are globally tree-like: for any > 0, there is an integer g( ) such that every string graph with n vertices and girth at least g( ) has at most (1 + )n edges.
Jacob Fox, János Pach
Added 01 Mar 2011
Updated 01 Mar 2011
Type Journal
Year 2010
Where CPC
Authors Jacob Fox, János Pach
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