3 citations · 3 across the 8 of their papers we have counts for
4 papers · 1 filter
On efficient graph covers and steered random walks
Nathan Tung, Richard Ueltzen
We prove that the vertices of any -vertex graph can be partitioned into pieces of radius such that the sum of the sizes of their closed neighborhoods is at most…
Linear equations and chromatic thresholds in sets
Nathan Tung
We derive sparse analogs of several Roth-type results, showing that they hold in sets of near-maximum size. It is shown that if a set is free of pairwise distinct solut…
Randomly piercing algebraic sets
Daniel Altman, Nathan Tung
We show, for example, that if one samples \[\frac{\log p}{2\log(1+(p-1)^{-1})} \cdot n^2(1 + o_{n\to \infty}(1))\] points in at random then asymptotically almost s…
Coloring sparse random Cayley graphs
Nathan Tung
It is shown that there exists so that the Cayley graph over any finite abelian group generated by random elements is properly 3-colorable with high probabi…