Radoš Radoičić

Relaxing Planarity for Topological Graphs

According to Euler’s formula, every planar graph with n vertices has at most O(n) edges. How much can we relax the condition of planarity without violating the conclusion? After surveying some classical and recent results of this kind, we prove that every graph of n vertices, which can be drawn in the plane without three pairwise crossing edges, has at most O(n) edges. For straight-line drawings, this statement has been established by Agarwal et al., using a more complicated argument, but for the general case previously no bound better than O(n 3/2) was known.

Rainbow Arithmetic Progressions and Anti-Ramsey Results

The van der Waerden theorem in Ramsey theory states that, for every

Note on the Chromatic Number of the Space

k

A dense planar point set from iterated line intersections

and

Note: Rainbow solutions to the Sidon equation

t

On the diameter of separated point sets with many nearly equal distances

and sufficiently large

Monotone paths in line arrangements

N

Exponentiation of Conditional Expectations Under Stochastic Volatility

, every

Nearly equal distances and Szemerédi's regularity lemma

k

Tighter Bounds for Implied Volatility

-colouring of