## View abstract

### Session I.3 - Graph Theory and Combinatorics

Tuesday, June 13, 15:00 ~ 15:30

## 6th diagonal Ramsey number is at most 147

### Jan Volec

#### Czech Technical University in Prague, Czeh Republic   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak9e4d977cdfbb6b8da979f49d010b4ba0').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy9e4d977cdfbb6b8da979f49d010b4ba0 = 'j&#97;n.v&#111;l&#101;c' + '&#64;'; addy9e4d977cdfbb6b8da979f49d010b4ba0 = addy9e4d977cdfbb6b8da979f49d010b4ba0 + 'fjf&#105;' + '&#46;' + 'cv&#117;t' + '&#46;' + 'cz'; var addy_text9e4d977cdfbb6b8da979f49d010b4ba0 = 'j&#97;n.v&#111;l&#101;c' + '&#64;' + 'fjf&#105;' + '&#46;' + 'cv&#117;t' + '&#46;' + 'cz';document.getElementById('cloak9e4d977cdfbb6b8da979f49d010b4ba0').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy9e4d977cdfbb6b8da979f49d010b4ba0 + '\'>'+addy_text9e4d977cdfbb6b8da979f49d010b4ba0+'<\/a>';

The diagonal Ramsey number $R(k)$ is the smallest order of a complete graph such that any $2$-coloring of its edges contain a monchromatic complete subgraph of order $k$. It is well known that $a \cdot k 2^{k/2} \lt R(k) \lt (4-b)^k$ for some absolute constants $a \gt 0$ and $b \gt 0$. On the other extreme, we know that $R(3)=6$ and $R(4)=18$, but already the exact value of $R(5)$ is not known. Determining the exact value of $R(k)$ for small values of $k\ge5$ is a challenging problem, and a well known quote of Erdős says that if aliens invade the Earth and demand within a year the exact value of $R(6)$, then we should rather attempt to destroy the aliens than determine $R(6)$. In this talk, we use the flag algebra method to show $R(6)$ is at most $147$ improving on the previous upper bound $R(6) \le 161$.

Joint work with Sergey Norin (McGill University) and Jeremie Turcotte (McGill University).