52 citations · 65 across the 12 of their papers we have counts for
8 papers · 1 filter
A note on the largest bipartite subgraph in point-hyperplane incidence graphs
Thao T. Do
Given points and hyperplanes in , if there are many incidences, we expect to find a big cluster in their incidence graph. Apfelbaum and Sharir found…
Nondegenerate spheres in four dimensions
Thao T. Do
Non-degeneracy was first defined for hyperplanes by Elekes-Tóth, and later extended to spheres by Apfelbaum-Sharir: given a set of points in and some $β\in(0…
A General Incidence Bound in and Related Problems
Thao Do, Adam Sheffer
We derive a general upper bound for the number of incidences with -dimensional varieties in . The leading term of this new bound generalizes previous bounds for t…
On the k-planar local crossing number
John Asplund, Thao do, Arran Hamm +1
Given a fixed positive integer , the -planar local crossing number of a graph , denoted by , is the minimum positive integer such that can be deco…
The k-planar crossing number of random graphs and random regular graphs
John Asplund, Thao Do, Arran Hamm +3
We give an explicit extension of Spencer's result on the biplanar crossing number of the Erdos-Renyi random graph . In particular, we show that the k-planar crossing number…
Representation Complexity of Semi-algebraic Graphs
Thao Do
The representation complexity of a bipartite graph is the minimum size over all possible ways to write as a (not necessarily disjoint) un…
Zarankiewicz's problem for semi-algebraic hypergraphs
Thao Do
Zarankiewicz's problem asks for the largest possible number of edges in a graph that does not contain a subgraph for a fixed positive integer . Recently, Fox, Pach, Sh…
Extending Erdős- Beck's theorem to higher dimensions
Thao Do
Erdős-Beck theorem states that points in the plane with at most points collinear define at least lines for some positive constant . In this paper, we will prese…