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SUMMARY:Matthew Jenssen (University of Birmingham)
DTSTART:20200608T130000Z
DTEND:20200608T140000Z
DTSTAMP:20260423T021030Z
UID:EPC/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/9/">A pr
 oof of the Upper Matching Conjecture for large graphs</a>\nby Matthew Jens
 sen (University of Birmingham) as part of Extremal and probabilistic combi
 natorics webinar\n\n\nAbstract\nWe show that the `Upper Matching Conjectur
 e' of Friedland\, Krop\, and Markström and the analogous conjecture of Ka
 hn for independent sets in regular graphs hold for all large enough graphs
  as a function of the degree. That is\, for every $d$ and every large enou
 gh $n$ divisible by $2d$\, a union of $n \\over 2d$ copies of the complete
  $d$-regular bipartite graph maximises the number of independent sets and 
 matchings of any given size over all $d$-regular graphs on $n$ vertices. F
 or the proof\, we'll discuss two different approaches to these problems\, 
 both inspired by statistical physics. This is joint work with Ewan Davies 
 and Will Perkins.\n
LOCATION:https://researchseminars.org/talk/EPC/9/
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