Minki Kim (김민기), Rainbow paths and rainbow matchings
Room B232 IBS (기초과학연구원)We prove that if $n \geq 3$, then any family of $3n-3$ sets of matchings of size $n$ in any graph has a rainbow matching of size $n$. This improves …
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Discrete Math Seminar
Kevin Hendrey, A unified half-integral Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups
Room B232 IBS (기초과학연구원)Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all …
Debsoumya Chakraborti, Some classical problems in graph saturation
Room B232 IBS (기초과학연구원)Graph saturation is one of the oldest areas of investigation in extremal combinatorics. A graph $G$ is called $F$-saturated if $G$ does not contain a subgraph isomorphic to $F$, but …
Se-Young Yun (윤세영), Regret in Online Recommendation Systems
Room B232 IBS (기초과학연구원)We propose a theoretical analysis of recommendation systems in an online setting, where items are sequentially recommended to users over time. In each round, a user, randomly picked from a …
Hong Liu (刘鸿), Nested cycles with no geometric crossing
Room B232 IBS (기초과학연구원)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 $C_2$, …
Casey Tompkins, 3-uniform hypergraphs avoiding a cycle of length four
Room B232 IBS (기초과학연구원)We show that that the maximum number of of edges in a $3$-uniform hypergraph without a Berge-cycle of length four is at most $(1+o(1)) \frac{n^{3/2}}{\sqrt{10}}$. This improves earlier estimates by …
Rutger Campbell, Matroid orientability and representability
Room B232 IBS (기초과학연구원)In this talk we will have a brief introduction to oriented matroids and their relation to real-representability.
William Overman, Some Ordered Ramsey Numbers of Graphs on Four Vertices
Room B232 IBS (기초과학연구원)Ordered Ramsey numbers were introduced in 2014 by Conlon, Fox, Lee, and Sudakov. Their results included upper bounds for general graphs and lower bounds showing separation from classical Ramsey numbers. We …
Sang-il Oum (엄상일), What is an isotropic system?
Room B232 IBS (기초과학연구원)Bouchet introduced isotropic systems in 1983 unifying some combinatorial features of binary matroids and 4-regular graphs. The concept of isotropic system is a useful tool to study vertex-minors of graphs …
Jungho Ahn (안정호), Well-partitioned chordal graphs with the obstruction set and applications
Room B232 IBS (기초과학연구원)We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set …