11 citations · 16 across the 11 of their papers we have counts for
5 papers · 1 filter
A solution to Ringel's circle problem
James Davies, Chaya Keller, Linda Kleist +2
We construct families of circles in the plane such that their tangency graphs have arbitrarily large girth and chromatic number. This provides a strong negative answer to Ringel's…
The tripartite-circle crossing number of graphs with two small partition classes
Charles Camacho, Silvia Fernández-Merchant, Marija Jelić Milutinović +4
A tripartite-circle drawing of a tripartite graph is a drawing in the plane, where each part of a vertex partition is placed on one of three disjoint circles, and the edges do not…
Bounding the tripartite-circle crossing number of complete tripartite graphs
Charles Camacho, Silvia Fernández-Merchant, Marija Jelić Milutinović +4
A tripartite-circle drawing of a tripartite graph is a drawing in the plane, where each part of a vertex partition is placed on one of three disjoint circles, and the edges do not…
Rainbow cycles in flip graphs
Stefan Felsner, Linda Kleist, Torsten Mütze +1
The flip graph of triangulations has as vertices all triangulations of a convex -gon, and an edge between any two triangulations that differ in exactly one edge. An -rainbow…
Upper and Lower Bounds on Long Dual-Paths in Line Arrangements
Udo Hoffmann, Linda Kleist, Tillmann Miltzow
Given a line arrangement with lines, we show that there exists a path of length in the dual graph of formed by its faces. This bound is tight u…