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BEGIN:VEVENT
SUMMARY:Hong Liu (Warwick)
DTSTART:20201211T140000Z
DTEND:20201211T150000Z
DTSTAMP:20260423T003233Z
UID:WCS/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WCS/14/">Ext
 remal density for sparse minors and subdivisions</a>\nby Hong Liu (Warwick
 ) as part of Warwick Combinatorics Seminar\n\n\nAbstract\nHow dense a grap
 h has to be to necessarily contain (topological) minors of a given graph $
 H$? When $H$ is a complete graph\, this question is well understood by res
 ult of Kostochka/Thomason for clique minor\, and result of Bollobas-Thomas
 on/Komlos-Szemeredi for topological minor. The situation is a lot less cle
 ar when $H$ is a sparse graph. We will present a general result on optimal
  density condition forcing (topological) minors of a wide range of sparse 
 graphs. As corollaries\, we resolve several questions of Reed and Wood on 
 embedding sparse minors. Among others\,\n\n      - $(1+o(1))t^2$ average d
 egree is sufficient to force the $t\\times t$ grid as a topological minor\
 ;\n\n      - $(3/2+o(1))t$ average degree forces $every$ $t$-vertex planar
  graph as a minor\, and the constant $3/2$ is optimal\, furthermore\, surp
 risingly\, the value is the same for $t$-vertex graphs embeddable on any f
 ixed surface\;\n\n      - a universal bound of $(2+o(1))t$ on average degr
 ee forcing $every$ $t$-vertex graph in $any$ nontrivial minor-closed famil
 y as a minor\, and the constant 2 is best possible by considering graphs w
 ith given treewidth.\n\nJoint work with John Haslegrave and Jaehoon Kim.\n
LOCATION:https://researchseminars.org/talk/WCS/14/
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