# Dimitrios M. Thilikos, Bounding Obstructions sets: the cases of apices of minor closed classes

## May 26 Wednesday @ 5:00 PM - 6:00 PM KST

Zoom ID: 934 3222 0374 (ibsdimag)

### Speaker

Given a minor-closed graph class ${\cal G}$, the (minor) obstruction of ${\cal G}$ is the set of all minor-minimal graphs not in ${\cal G}$. Given a non-negative integer $k$, we define the $k$-apex of ${\cal A}$ as the class containing every graph $G$ with a set $S$ of vertices whose removal from $G$ gives a graph on ${\cal G}$. We prove that every obstruction of the $k$-apex of ${\cal G}$ has size bounded by some 4-fold exponential function of $p(k)$ where p is a polynomial function whose degree depends on the size of the minor-obstructions of ${\cal G}$. This bound drops to a 2-fold exponential one when ${\cal G}$ excludes some apex graph as a minor (i.e., a graph in the $1$-apex of planar graphs).

Joint work with Ignasi Sau and Giannos Stamoulis.

## Details

Date:
May 26 Wednesday
Time:
5:00 PM - 6:00 PM KST
Event Category:
Event Tags:

## Venue

Zoom ID: 934 3222 0374 (ibsdimag)

## Organizer

O-joung Kwon (권오정)
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