eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-06-20
56:1
56:15
10.4230/LIPIcs.SoCG.2017.56
article
Coloring Curves That Cross a Fixed Curve
Rok, Alexandre
Walczak, Bartosz
We prove that for every integer t greater than or equal to 1, the class of intersection graphs of curves in the plane each of which crosses a fixed curve in at least one and at most t points is chi-bounded. This is essentially the strongest chi-boundedness result one can get for this kind of graph classes. As a corollary, we prove that for any fixed integers k > 1 and t > 0, every k-quasi-planar topological graph on n vertices with any two edges crossing at most t times has O(n log n) edges.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol077-socg2017/LIPIcs.SoCG.2017.56/LIPIcs.SoCG.2017.56.pdf
String graphs
chi-boundedness
k-quasi-planar graphs