GD 2001: Graph Drawing pp 247-260

# Recognizing String Graphs Is Decidable

• János Pach
• Géza Tóth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2265)

## Abstract

A graph is called a string graph if its vertices can be represented by continuous curves (“strings”)in the plane so that two of them cross each other if and only if the corresponding vertices are adjacent. It is shown that there exists a recursive function f(n)with the property that every string graph of n vertices has a representation in which any two curves cross at most f(n)times. We obtain as a corollary that there is an algorithm for deciding whether a given graph is a string graph. This solves an old problem of (1959), (1966), and G(1971).

## Keywords

Intersection Graph Combinatorial Theory Permutation Graph Clockwise Order Delete Vertex
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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