## September 2019

### Kevin Hendrey, The minimum connectivity forcing forest minors in large graphs

Room B232 IBS (기초과학연구원)

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 $\tau(G)\leq ## March 2020 ### Kevin Hendrey, Covering radius in the Hamming permutation space Room B232 IBS (기초과학연구원) Our problem can be described in terms of a two player game, played with the set$\mathcal{S}_n$of permutations on$\{1,2,\dots,n\}$. First, Player 1 selects a subset$S$of$\mathcal{S}_n$and shows it to Player 2. Next, Player 2 selects a permutation$p$from$\mathcal{S}_n$as different as possible from the permutations in$S$, and shows it to Player ## March 2021 ### Kevin Hendrey, A unified half-integral Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups Room B232 IBS (기초과학연구원) Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold if we restrict to odd cycles. However, in 1999, Reed proved an analogue for odd cycles by relaxing packing ## September 2021 ### Kevin Hendrey, Extremal functions for sparse minors Room B232 IBS (기초과학연구원) The extremal function$c(H)$of a graph$H$is the supremum of densities of graphs not containing$H$as a minor, where the density of a graph is the ratio of the number of edges to the number of vertices. Myers and Thomason (2005), Norin, Reed, Thomason and Wood (2020), and Thomason and Wales (2019) ## March 2022 ### Kevin Hendrey, A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups (revisited) Room B232 IBS (기초과학연구원) This talk follows on from the recent talk of Pascal Gollin in this seminar series, but will aim to be accessible for newcomers. Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. By ## July 2022 ### Kevin Hendrey, Product Structure of Graph Classes with Bounded Treewidth Room B232 IBS (기초과학연구원) The strong product$G\boxtimes H$of graphs$G$and$H$is the graph on the cartesian product$V(G)\times V(H)$such that vertices$(v,w)$and$(x,y)$are adjacent if and only if$\max\{d_G(v,x),d_H(w,y)\}=1\$. Graph product structure theory aims to describe complicated graphs in terms of subgraphs of strong products of simpler graphs. This area of research was initiated

기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209