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4 papers · 2 filters
Biased orientation games
Ido Ben-Eliezer, Michael Krivelevich, Benny Sudakov
We study biased {\em orientation games}, in which the board is the complete graph , and Maker and Breaker take turns in directing previously undirected edges of . At the…
Nonnegative k-sums, fractional covers, and probability of small deviations
Noga Alon, Hao Huang, Benny Sudakov
More than twenty years ago, Manickam, Miklós, and Singhi conjectured that for any integers satisfying , every set of real numbers with nonnegative sum has at…
Simple Proofs of Classical Theorems in Discrete Geometry via the Guth--Katz Polynomial Partitioning Technique
Haim Kaplan, Jiří Matoušek, Micha Sharir
Recently Guth and Katz \cite{GK2} invented, as a step in their nearly complete solution of Erdős's distinct distances problem, a new method for partitioning finite point sets in $\…
Longest cycles in sparse random digraphs
Michael Krivelevich, Eyal Lubetzky, Benny Sudakov
Long paths and cycles in sparse random graphs and digraphs were studied intensively in the 1980's. It was finally shown by Frieze in 1986 that the random graph $\cG(n,p)$ with $p=c…