Zixiang Xu (徐子翔), Multilinear polynomial methods and stability results on set systems
Room B332 IBS (기초과학연구원)In 1966, Kleitman established that if
In 1966, Kleitman established that if
A major goal of additive combinatorics is to understand the structures of subsets A of an abelian group G which has a small doubling K = |A+A|/|A|. Freiman's celebrated theorem first provided a structural characterization of sets with small doubling over the integers, and subsequently Ruzsa in 1999 proved an analog for abelian groups with …
The peaceable queens problem asks to determine the maximum number
A replacement action is a function
The group
An induced packing of cycles in a graph is a set of vertex-disjoint cycles such that the graph has no edge between distinct cycles of the set. The classic Erdős-Pósa theorem shows that for every positive integer
A family
We present a full characterization of the unavoidable induced subgraphs of graphs with large pathwidth. This consists of two results. The first result says that for every forest H, every graph of sufficiently large pathwidth contains either a large complete subgraph, a large complete bipartite induced minor, or an induced minor isomorphic to H. The …
In 1996, Reed, Robertson, Seymour and Thomas proved Younger's Conjecture, which states that for all directed graphs D, there exists a function f such that if D does not contain k disjoint cycles, D contains a feedback vertex set, i.e. a subset of vertices whose deletion renders the graph acyclic, of size bounded by f(k). …
Since the proof of the graph minor structure theorem by Robertson and Seymour in 2004, its underlying ideas have found applications in a much broader range of settings than their original context. They have driven profound progress in areas such as vertex minors, pivot minors, matroids, directed graphs, and 2-dimensional simplicial complexes. In this talk, …