## View abstract

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

Wednesday, June 14, 14:30 ~ 15:00

## The 4-color Ramsey Multiplicity of Triangles

### Aldo Kiem

#### Zuse Institute Berlin and TU Berlin, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak3e0e40d6cd1f61af20b4bddce58b4b6b').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy3e0e40d6cd1f61af20b4bddce58b4b6b = 'k&#105;&#101;m' + '&#64;'; addy3e0e40d6cd1f61af20b4bddce58b4b6b = addy3e0e40d6cd1f61af20b4bddce58b4b6b + 'z&#105;b' + '&#46;' + 'd&#101;'; var addy_text3e0e40d6cd1f61af20b4bddce58b4b6b = 'k&#105;&#101;m' + '&#64;' + 'z&#105;b' + '&#46;' + 'd&#101;';document.getElementById('cloak3e0e40d6cd1f61af20b4bddce58b4b6b').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy3e0e40d6cd1f61af20b4bddce58b4b6b + '\'>'+addy_text3e0e40d6cd1f61af20b4bddce58b4b6b+'<\/a>';

In 1959 Goodman established that asymptotically, in any two-edge-coloring of the complete graph, at least a quarter of all triangles must be monochromatic. This initiated the much studied Ramsey Multiplicity Problem and was extended in 2013 by Cummings et al. to three-edge-colorings. In this talk, we will extend this results to triangles in four-edge-colorings and explore the computational challenges of scaling up flag-algebra based proofs.

Joint work with Sebastian Pokutta (Zuse Institute Berlin and TU Berlin, Germany) and Christoph Spiegel (Zuse Institute Berlin, Germany).