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Hong Liu (刘鸿), Nested cycles with no geometric crossing
March 22 Monday @ 4:30 PM - 5:30 PM KST
In 1975, Erdős asked the following question: what is the smallest function $f(n)$ for which all graphs with $n$ vertices and $f(n)$ edges contain two edge-disjoint cycles $C_1$ and $C_2$, such that the vertex set of $C_2$ is a subset of the vertex set of $C_1$ and their cyclic orderings of the vertices respect each other? We prove the optimal linear bound $f(n)=O(n)$ using sublinear expanders.
This is joint work with Irene Gil Fernández, Jaehoon Kim and Younjin Kim.