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DTSTART;TZID=Asia/Seoul:20210526T170000
DTEND;TZID=Asia/Seoul:20210526T180000
DTSTAMP:20260420T111956
CREATED:20210424T122241Z
LAST-MODIFIED:20240707T081338Z
UID:3986-1622048400-1622052000@dimag.ibs.re.kr
SUMMARY:Dimitrios M. Thilikos\, Bounding Obstructions sets: the cases of apices of minor closed classes
DESCRIPTION: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). \nJoint work with Ignasi Sau and Giannos Stamoulis.
URL:https://dimag.ibs.re.kr/event/2021-05-26/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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