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4 papers · 2 filters
Directed graphs without short cycles
Jacob Fox, Peter Keevash, Benny Sudakov
For a directed graph without loops or parallel edges, let denote the size of the smallest feedback arc set, i.e., the smallest subset such that $G \sm X…
Economical toric spines via Cheeger's Inequality
Noga Alon, Bo'az Klartag
Let denote the graph whose set of vertices is , where two distinct vertices are adjacent iff they are either equal or adjacent in $C_m…
Hypergraph Ramsey numbers
David Conlon, Jacob Fox, Benny Sudakov
The Ramsey number r_k(s,n) is the minimum N such that every red-blue coloring of the k-tuples of an N-element set contains either a red set of size s or a blue set of size n, where…
Unavoidable patterns
Jacob Fox, Benny Sudakov
Let \mathcal{F}_k denote the family of 2-edge-colored complete graphs on 2k vertices in which one color forms either a clique of order k or two disjoint cliques of order k. Bollobá…