기초과학연구원 이산수학그룹
There has been a raising interest on the study of perfect matchings in uniform hypergraphs in the past two decades, including extremal problems and their algorithmic versions. I will introduce the problems and some recent developments.
Amazon drivers hit the road every day, each taking a Prime van in a traveling salesman problem tour through 150 or more customer stops. But even a whisper of the TSP strikes fear in the heart of the computing world. A Washington Post article reported it would take "1,000 years to compute the most efficient …
We prove a conjecture of Bonamy, Bousquet, Pilipczuk, Rzążewski, Thomassé, and Walczak, that for every graph $H$, there is a polynomial $p$ such that for every positive integer $s$, every graph of average degree at least $p(s)$ contains either $K_{s,s}$ as a subgraph or contains an induced subdivision of $H$. This improves upon a result …
Let $\mathcal{G}$ and $\mathcal{H}$ be minor-closed graphs classes. The class $\mathcal{H}$ has the Erdős-Pósa property in $\mathcal{G}$ if there is a function $f : \mathbb{N} \to \mathbb{N}$ such that every graph $G$ in $\mathcal{G}$ either contains (a packing of) $k$ disjoint copies of some subgraph minimal graph $H \not\in \mathcal{H}$ or contains (a covering of) …
Bollobás proved that for every $k$ and $\ell$ such that $k\mathbb{Z}+\ell$ contains an even number, an $n$-vertex graph containing no cycle of length $\ell \bmod k$ can contain at most a linear number of edges. The precise (or asymptotic) value of the maximum number of edges in such a graph is known for very few …