A Separator Theorem for String Graphs and Its Applications
نویسندگان
چکیده
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(m √ 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 2 > 0, there is an integer g(2) such that every string graph with n vertices and girth at least g(2) has at most (1 + 2)n edges.
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