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- W4300892252 abstract "A {em 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 {em almost all} string graphs on $n$ vertices can be partitioned into {em five} cliques such that some pair of them is not connected by any edge ($nrightarrowinfty$). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that {em almost all} string graphs on $n$ vertices are intersection graphs of plane convex sets." @default.
- W4300892252 created "2022-10-04" @default.
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- W4300892252 date "2018-03-18" @default.
- W4300892252 modified "2023-10-06" @default.
- W4300892252 title "Almost all string graphs are intersection graphs of plane convex sets" @default.
- W4300892252 doi "https://doi.org/10.48550/arxiv.1803.06710" @default.
- W4300892252 hasPublicationYear "2018" @default.
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