output
20022009
most citedQuantum ESPRESSO: a modular and open-source software project for quantum simulations of materials

29.3k citations

Showing 2007 · math.COShow all

9 papers · 2 filters

math.CO2007

Discrete Kakeya-type problems and small bases

Noga Alon, Boris Bukh, Benny Sudakov

A subset U of a group G is called k-universal if U contains a translate of every k-element subset of G. We give several nearly optimal constructions of small k-universal sets, and…

math.CO200710 cited

Harmonic morphisms and hyperelliptic graphs

Matthew Baker, Serguei Norine

We study harmonic morphisms of graphs as a natural discrete analogue of holomorphic maps between Riemann surfaces. We formulate a graph-theoretic analogue of the classical Riemann-…

math.CO2007

Density theorems for bipartite graphs and related Ramsey-type results

Jacob Fox, Benny Sudakov

In this paper, we present several density-type theorems which show how to find a copy of a sparse bipartite graph in a graph of positive density. Our results imply several new boun…

math.CO2007

Ramsey numbers and the size of graphs

Benny Sudakov

For two graph H and G, the Ramsey number r(H, G) is the smallest positive integer n such that every red-blue edge coloring of the complete graph K_n on n vertices contains either a…

math.CO20071 cited

Embedding nearly-spanning bounded degree trees

Noga Alon, Michael Krivelevich, Benny Sudakov

We derive a sufficient condition for a sparse graph G on n vertices to contain a copy of a tree T of maximum degree at most d on (1-ε)n vertices, in terms of the expansion properti…

math.CO2007

On graphs with subgraphs of large independence numbers

Noga Alon, Benny Sudakov

Let G be a graph on n vertices in which every induced subgraph on s=\log^3 n vertices has an independent set of size at least t=\log n. What is the largest q=q(n) so that every suc…