Jun Gao, Number of (k-1)-cliques in k-critical graph
Room B332 IBS (기초과학연구원)We prove that for $n>k\geq 3$, if $G$ is an $n$-vertex graph with chromatic number $k$ but any its proper subgraph has smaller chromatic number, then $G$ contains at most …
Loading view.
Raphael Steiner, Congruence-constrained subdivisions in digraphs
Zoom ID: 869 4632 6610 (ibsdimag)I will present the short proof from that for every digraph F and every assignment of pairs of integers $(r_e,q_e)_{e\in A(F)}$ to its arcs, there exists an integer $N$ such …
Bjarne Schülke, A local version of Katona’s intersection theorem
Room B332 IBS (기초과학연구원)Katona's intersection theorem states that every intersecting family $\mathcal F\subseteq^{(k)}$ satisfies $\vert\partial\mathcal F\vert\geq\vert\mathcal F\vert$, where $\partial\mathcal F=\{F\setminus x:x\in F\in\mathcal F\}$ is the shadow of $\mathcal F$. Frankl conjectured that for …
Dömötör Pálvölgyi, C-P3O: Orientation of convex sets and other good covers
Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]We introduce a novel definition of orientation on the triples of a family of pairwise intersecting planar convex sets and study its properties. In particular, we compare it to other …
Sebastian Wiederrecht, Killing a vortex
Room B332 IBS (기초과학연구원)The Structural Theorem of the Graph Minors series of Robertson and Seymour asserts that, for every $t\in\mathbb{N},$ there exists some constant $c_{t}$ such that every $K_{t}$-minor-free graph admits a tree …
Mehtaab Sawhney, Anticoncentration in Ramsey graphs and a proof of the Erdős-McKay conjecture
Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]An $n$-vertex graph is called $C$-Ramsey if it has no clique or independent set of size $C\log_2 n$ (i.e., if it has near-optimal Ramsey behavior). We study edge-statistics in Ramsey …
Alexander Clifton, Ramsey Theory for Diffsequences
Room B332 IBS (기초과학연구원)Van der Waerden's theorem states that any coloring of $\mathbb{N}$ with a finite number of colors will contain arbitrarily long monochromatic arithmetic progressions. This motivates the definition of the van …
Santiago Guzmán-Pro, Local expressions of graphs classes
Zoom ID: 869 4632 6610 (ibsdimag)A common technique to characterize hereditary graph classes is to exhibit their minimal obstructions. Sometimes, the set of minimal obstructions might be infinite, or too complicated to describe. For instance, for any …
Zixiang Xu (徐子翔), On the degenerate Turán problems
Room B332 IBS (기초과학연구원)For a graph $F$, the Turán number is the maximum number of edges in an $n$-vertex simple graph not containing $F$. The celebrated Erdős-Stone-Simonovits Theorem gives that \ where $\chi(F)$ is the …
Konstantin Tikhomirov, A remark on the Ramsey number of the hypercube
Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]A well-known conjecture of Burr and Erdős asserts that the Ramsey number $r(Q_n)$ of the hypercube $Q_n$ on $2^n$ vertices is of the order $O(2^n)$. In this paper, we show that …