# A Ramsey-type Theorem on the Max-Cut Value of d-Regular Graphs

@article{Carlson2018ART, title={A Ramsey-type Theorem on the Max-Cut Value of d-Regular Graphs}, author={Charles Carlson and Alexandra Kolla and Luca Trevisan}, journal={ArXiv}, year={2018}, volume={abs/1810.10044} }

In this paper we study the problem of finding large cuts in $K_r$-free graphs with max degree $d$. We show that such graphs always have cuts which cut a $1/2+\Omega(1/d^{1-1/d^{r-2}})$ fraction of edges. This generalizes known results for $K_3$-free graphs. A key component of this result is showing that graphs with few triangles also have non-trivially good cuts.

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## Max-Cut in Degenerate H-Free Graphs

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