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SUMMARY:Oliver Janzer (University of Cambridge)
DTSTART:20200820T080000Z
DTEND:20200820T090000Z
DTSTAMP:20260423T035022Z
UID:SCMSComb/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SCMSComb/9/"
 >Rainbow Turán number of even cycles</a>\nby Oliver Janzer (University of
  Cambridge) as part of SCMS Combinatorics Seminar\n\n\nAbstract\nThe rainb
 ow Tur\\'an number $\\mathrm{ex}^*(n\,H)$ of a\ngraph $H$ is the maximum p
 ossible number of edges in a properly\nedge-coloured $n$-vertex graph with
  no rainbow subgraph isomorphic to\n$H$. We prove that for any integer $k\
 \geq 2$\,\n$\\mathrm{ex}^*(n\,C_{2k})=O(n^{1+1/k})$. This is tight and est
 ablishes a\nconjecture of Keevash\, Mubayi\, Sudakov and Verstra\\"ete. We
  use the same\nmethod to prove several other conjectures in various topics
 . For\nexample\, we give an upper bound for the Tur\\'an number of the blo
 w-ups\nof even cycles\, which can be used to disprove a conjecture of Erd\
 \H os\nand Simonovits.\n\npassword 111317\n
LOCATION:https://researchseminars.org/talk/SCMSComb/9/
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