기초과학연구원 이산수학그룹
The annual conference on Combinatorics Workshop (조합론 학술대회) began in 2004 by the Yonsei University BK21 Research Group. This year it will take place in Songdo, Incheon, August 13-15, 2019. Due to the capacity (50 persons) of the place, we are able to limit your registration. In principle, registration is on a first-come, first-served basis. …
In this talk we shall discuss how quickly the genus of the Erdős-Rényi random graph grows as the number of edges increases and how dramatically a small number of random edges can increase the genus of a randomly perturbed graph. (Joint work with Chris Dowden and Michael Krivelevich)
Given a graph $G$, we define $\textrm{ex}_c(G)$ to be the minimum value of $t$ for which there exists a constant $N(t,G)$ such that every $t$-connected graph with at least $N(t,G)$ vertices contains $G$ as a minor. The value of $\textrm{ex}_c(G)$ is known to be tied to the vertex cover number $\tau(G)$, and in fact $\tau(G)\leq …
Let $F$ and $H$ be graphs. The subgraph counting function $\operatorname{ex}(n,H,F)$ is defined as the maximum possible number of subgraphs $H$ in an $n$-vertex $F$-free graph. This function is a direct generalization of the Turán function as $\operatorname{ex}(n,F)=\operatorname{ex}(n,K_2,F)$. The systematic study of $\operatorname{ex}(n,H,F)$ was initiated by Alon and Shikhelman in 2016 who generalized several classical …
Given a graph $G$, there are several natural hypergraph families one can define. Among the least restrictive is the family $BG$ of so-called Berge copies of the graph $G$. In this talk, we discuss Turán problems for families $BG$ in $r$-uniform hypergraphs for various graphs $G$. In particular, we are interested in general results in …
A well-known Ramsey-type puzzle for children is to prove that among any 6 people either there are 3 who know each other or there are 3 who do not know each other. More generally, a graph $G$ arrows a graph $H$ if for any coloring of the edges of $G$ with two colors, there is a …
A graph or graph property is $\ell$-reconstructible if it is determined by the multiset of all subgraphs obtained by deleting $\ell$ vertices. Apart from the famous Graph Reconstruction Conjecture, Kelly conjectured in 1957 that for each $\ell\in\mathbb N$, there is an integer $n=n(\ell)$ such that every graph with at least $n$ vertices is $\ell$-reconstructible. We show that for …
For a graph $H$ and an integer $k\ge1$, the $k$-color Ramsey number $R_k(H)$ is the least integer $N$ such that every $k$-coloring of the edges of the complete graph $K_N$ contains a monochromatic copy of $H$. Let $C_m$ denote the cycle on $m\ge4 $ vertices. For odd cycles, Bondy and Erd\H{o}s in 1973 conjectured that …
For a graph $H$, its homomorphism density in graphs naturally extends to the space of two-variable symmetric functions $W$ in $L^p$, $p\geq e(H)$, denoted by $t_H(W)$. One may then define corresponding functionals $\|W\|_{H}:=|t_H(W)|^{1/e(H)}$ and $\|W\|_{r(H)}:=t_H(|W|)^{1/e(H)}$ and say that $H$ is (semi-)norming if $\|.\|_{H}$ is a (semi-)norm and that $H$ is weakly norming if $\|.\|_{r(H)}$ is …
Focus Session @ 2019 KMS Annual MeetingA focus session "Extremal and Structural Graph Theory" at the 2019 KMS Annual Meeting is organized by Sang-il Oum. URL: http://www.kms.or.kr/meetings/fall2019/SpeakersIlkyoo Choi (최일규), Hankuk University of Foreign StudiesKevin Hendrey, IBS Discrete Mathematics GroupPascal Gollin, IBS Discrete Mathematics GroupJaehoon Kim (김재훈), KAISTRingi Kim (김린기), KAISTSeog-Jin Kim (김석진), Konkuk UniversityO-joung Kwon (권오정), Incheon …
