52 citations · 65 across the 12 of their papers we have counts for
12 papers
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…
Sets Characterized by Missing Sums and Differences in Dilating Polytopes
Thao Do, Archit Kulkarni, Steven J. Miller +3
A sum-dominant set is a finite set of integers such that . As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to…
Sums and differences of correlated random sets
Thao Do, Archit Kulkarni, Steven J. Miller +2
Many fundamental questions in additive number theory (such as Goldbach's conjecture, Fermat's last theorem, and the Twin Primes conjecture) can be expressed in the language of sum…
Generalizing Zeckendorf's Theorem to f-decompositions
Philippe Demontigny, Thao Do, Archit Kulkarni +3
A beautiful theorem of Zeckendorf states that every positive integer can be uniquely decomposed as a sum of non-consecutive Fibonacci numbers , where , …
A Generalization of Fibonacci Far-Difference Representations and Gaussian Behavior
Philippe Demontigny, Thao Do, Archit Kulkarni +2
A natural generalization of base B expansions is Zeckendorf's Theorem: every integer can be uniquely written as a sum of non-consecutive Fibonacci numbers , with $F_{n+1}…