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Nearly tight bounds for induced subdivisions
Zach Hunter, Aleksa Milojević, Patryk Morawski +1
Subdivisions of complete graphs play a central role in combinatorics, having deep connections to structural, extremal, and topological aspects of graph theory. A celebrated conject…
The Mihail-Vazirani conjecture and strong edge-expansion in random polytopes
Micha Christoph, Sahar Diskin, Lyuben Lichev +1
We study the edge-expansion of the graph of a random polytope , defined as the convex hull of a random subset of the points in where every point is retaine…
Coloring small locally sparse degenerate graphs and related problems
Domagoj Bradač, Jacob Fox, Raphael Steiner +2
The classic upper bound on the chromatic number of -degenerate graphs is , shown to be tight by complete graphs. A natural question is whether this bound remains tight if o…
Color-avoiding directed paths in tournaments
Jacob Fox, Benny Sudakov, Yuval Wigderson
We study the following Ramsey-theoretic question: given a -coloring of the edges of a tournament, how long of a directed path can we guarantee whose edges avoid one of the color…
Set mappings for general graphs
Lior Gishboliner, Zhihan Jin, Benny Sudakov
The study of extremal problems for set mappings has a long history. It was introduced in 1958 by Erdős and Hajnal, who considered the case of cliques in graphs and hypergraphs. Rec…
Ramsey numbers of digraphs with local edge structure
Domagoj Bradač, Patryk Morawski, Benny Sudakov +1
One of the classical topics in graph Ramsey theory is the study of which -vertex graphs have Ramsey numbers that are linear in . In this paper, we consider this problem in th…