Julian Sahasrabudhe

Cambridge


On the multi-colour Ramsey numbers


Combinatorics Seminar


12th November 2024, 11:00 am – 12:00 pm
Fry Building, 2.04


The (multi-colour) Ramsey number R_r(k) is the minimum n so that every r-colouring of the edges of the complete graph on n vertices contains a monochromatic copy of K_r. Recently, Campos, Griffiths, Morris and Sahasrabudhe gave an exponential improvement for the classical 2-colour Ramsey numbers R(k) = R_2(k). However, this proof did not naturally generalize to more colours. In this talk I will discuss the proof of such a generalization. This new proof also simplifies and motivates several aspects of the original paper. The talk is based on joint work with Campos, Balister, Bollobás, Griffiths, Hurley, Morris and Tiba.






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