COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Combinatorics Seminar > The Multicolour Ramsey Number of a Long Odd Cycle

## The Multicolour Ramsey Number of a Long Odd CycleAdd to your list(s) Download to your calendar using vCal - Jozef Skokan (LSE)
- Thursday 12 October 2017, 14:30-15:30
- MR12.
If you have a question about this talk, please contact Andrew Thomason. For a graph $G$, the $k$-colour Ramsey number $R_k(G)$ is the least integer $N$ such that every $k$-colouring of the edges of the complete graph $K_N$ contains a monochromatic copy of $G$. Let $C_n$ denote the cycle on $n$ vertices. We show that for fixed $k\ge 3$ and $n$ odd and sufficiently large, $$R_k(C_n)=2^{k-1}(n-1)+1.$$ This generalises a result of Kohayakawa, Simonovits and Skokan and resolves a conjecture of Bondy and Erd\H{o}s for large $n$. We also establish a surprising correspondence between extremal $k$-colourings for this problem and perfect matchings in the hypercube $Q_k$. This allows us to in fact prove a stability-type generalisation of the above. The proof is analytic in nature, the first step of which is to use the Regularity Lemma to relate this problem in Ramsey theory to one in convex optimisation. This is joint work with Matthew Jenssen. This talk is part of the Combinatorics Seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- Combinatorics Seminar
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- MR12
- School of Physical Sciences
Note that ex-directory lists are not shown. |
## Other listsCRUK-CI Genomics Core seminar series Centre for Smart Infrastructure & Construction Seminars Caius MedSoc Talks: A Timeline of Medicine## Other talksEmbedding simply connected 2-complexes in 3-space Random cluster dynamics for the Ising model is rapidly mixing Global Governance and Grand Corruption: The International Politics and Policy of Looted Wealth Hunting Monsters Changing languages in European Higher Education: from official policies to unofficial classroom practices Healthcare Design |