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SUMMARY:The Multicolour Size Ramsey Number of a Path - Csongor Beke (Cambr
 idge)
DTSTART:20251127T143000Z
DTEND:20251127T153000Z
UID:TALK241285@talks.cam.ac.uk
CONTACT:103978
DESCRIPTION:The r-colour size Ramsey number of the path P_k is the smalles
 t m such that some m-edge graph G has a monochromatic P_k in every r-colou
 ring of its edges. The linearity in k has been established by Beck in 1983
 \, but finding the optimal r-dependence has been open since. The lower bou
 nd of cr^2 k by Krivelevich was suggested to be optimal\, while the best u
 pper bound of Dudek and Pralat is a factor of log r away. In this talk we 
 introduce a new colouring technique that\, somewhat surprisingly\, yields 
 a log r improvement in the lower bound\, solving the problem up to constan
 ts. Joint work with Anqi Li and Julian Sahasrabudhe.
LOCATION:MR12
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