3 papers
cs.CG2026
Separators for intersection graphs of spheres
Jacob Fox, Jonathan Tidor
We prove the existence of optimal separators for intersection graphs of balls and spheres in any dimension . One of our results is that if an intersection graph of spheres i…
math.CO2026
Coloring small locally sparse degenerate graphs and related problems
Domagoj Bradač, Jacob Fox, Raphael Steiner +2
The classic upper bound on the chromatic number of -degenerate graphs is , shown to be tight by complete graphs. A natural question is whether this bound remains tight if o…
math.CO2026
Color-avoiding directed paths in tournaments
Jacob Fox, Benny Sudakov, Yuval Wigderson
We study the following Ramsey-theoretic question: given a -coloring of the edges of a tournament, how long of a directed path can we guarantee whose edges avoid one of the color…