@article{7962, abstract = {A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n→∞). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets.}, author = {Pach, János and Reed, Bruce and Yuditsky, Yelena}, issn = {14320444}, journal = {Discrete and Computational Geometry}, number = {4}, pages = {888--917}, publisher = {Springer Nature}, title = {{Almost all string graphs are intersection graphs of plane convex sets}}, doi = {10.1007/s00454-020-00213-z}, volume = {63}, year = {2020}, }