Coloring Curves That Cross a Fixed Curve
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.
String graphs
chi-boundedness
k-quasi-planar graphs
56:1-56:15
Regular Paper
Alexandre
Rok
Alexandre Rok
Bartosz
Walczak
Bartosz Walczak
10.4230/LIPIcs.SoCG.2017.56
Creative Commons Attribution 3.0 Unported license
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