output
20022009
most citedNovel type of phase transition in a system of self-driven particles

7.5k citations

Showing 2007 · math.COShow all

6 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.CO20071 cited

Message passing for the coloring problem: Gallager meets Alon and Kahale

Sonny Ben-Shimon, Dan Vilenchik

Message passing algorithms are popular in many combinatorial optimization problems. For example, experimental results show that {\em survey propagation} (a certain message passing…

math.CO20076 cited

Vertex Percolation on Expander Graphs

Sonny Ben-Shimon, Michael Krivelevich

We say that a graph on vertices is a -expander for some constant if every of cardinality satisfies w…

math.CO20072 cited

Minors in expanding graphs

Michael Krivelevich, Benny Sudakov

Extending several previous results we obtained nearly tight estimates on the maximum size of a clique-minor in various classes of expanding graphs. These results can be used to sho…

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…