Hyunwoo Lee (이현우), Proof of the Erdős-Szemerédi sunflower conjecture
In the 1970s, Erdős and Szemerédi conjectured that for any $n \ge k-1\ge 2$, any collection of subsets of $$ not containing a $k$-sunflower has size at most $c_k^n$ for …
In the 1970s, Erdős and Szemerédi conjectured that for any $n \ge k-1\ge 2$, any collection of subsets of $$ not containing a $k$-sunflower has size at most $c_k^n$ for …
How close are the width parameters of a plane graph and its (geometric) dual? Research motivated by this question, known as the self-duality of width parameters, originated from the seminal …
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In the 1980s, Ron Graham asked whether every red/blue coloring of the positive integers contains a monochromatic Pythagorean triple and offered a $100 prize for the answer. The bounty was …
The codegree Turán density γ(F) of a k-uniform hypergraph F is the smallest γ ≥ 0 with the following property: if every set of k−1 vertices in an n-vertex k-uniform …
For any graph with maximum degree at most $\Delta$, a simple inductive argument shows that the graph can be properly colored using $\Delta+1$ colors. However, a direct implementation of this …
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