Quasiplanar graphs, string graphs, and the Erdős–Gallai problem

An r-quasiplanar graph is a graph drawn in the plane with no r pairwise crossing edges. Let s≥3 be an integer and r=2s. We prove that there is a constant C such that every r-quasiplanar graph with n≥r vertices has at most nCs−1logn2s−4 edges. A graph whose vertices are continuous curves in the plane...

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Bibliographic Details

Published in:	European journal of combinatorics Vol. 119; p. 103811
Main Authors:	Fox, Jacob, Pach, János, Suk, Andrew
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.06.2024
ISSN:	0195-6698
Online Access:	Get full text
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