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SUMMARY:Highly connected subgraphs in sparse graphs - Henry Liu (Central S
 outh University\, China)
DTSTART:20170209T143000Z
DTEND:20170209T153000Z
UID:TALK70308@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:Let G be a graph on n vertices with independence number $\\alp
 ha$. How large a k-connected subgraph must G contain? It turns out that if
  n is sufficiently large ($n>\\alpha^2 k$ will do)\, then G always contain
 s a\nk-connected subgraph on at least $n/\\alpha$ vertices. This is sharp\
 , since G might be the disjoint union of $\\alpha$ equally-sized cliques. 
 What if n is not\nsufficiently large? We shall present the (surprisingly c
 omplicated) answer when $\\alpha=2$ and $\\alpha=3$. Some open questions w
 ill also be presented.\n\n\nJoint work with Shinya Fujita (Yokohama City U
 niversity\, Japan) and Amites Sarkar (Western Washington University\, USA)
 .\n
LOCATION:MR12
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