## View abstract

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

Monday, June 12, 16:30 ~ 17:30

## Flag Algebras and Weighted Turán Theorems

### Bernard Lidický

#### Iowa State University, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak937e4cf1e630ed2947c131d09ec80f21').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy937e4cf1e630ed2947c131d09ec80f21 = 'l&#105;d&#105;cky' + '&#64;'; addy937e4cf1e630ed2947c131d09ec80f21 = addy937e4cf1e630ed2947c131d09ec80f21 + '&#105;&#97;st&#97;t&#101;' + '&#46;' + '&#101;d&#117;'; var addy_text937e4cf1e630ed2947c131d09ec80f21 = 'l&#105;d&#105;cky' + '&#64;' + '&#105;&#97;st&#97;t&#101;' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak937e4cf1e630ed2947c131d09ec80f21').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy937e4cf1e630ed2947c131d09ec80f21 + '\'>'+addy_text937e4cf1e630ed2947c131d09ec80f21+'<\/a>';

We study extensions of Turán Theorem in edge-weighted settings. A particular case of interest is when constraints on the weight of an edge come from the order of the largest clique containing it. These problems are motivated by Ramsey-Turán type problems. Using these results, we prove several new upper bounds on the Ramsey-Turán density of cliques. The talk will include an introduction to flag algebras that is one of the techniques useful for these type of problems.

Joint work with József Balogh (University of Illinois, USA) and Domagoj Bradač (ETH, Switzerland).