# Large Cuts with Local Algorithms on Triangle-Free Graphs

@article{Hirvonen2014LargeCW, title={Large Cuts with Local Algorithms on Triangle-Free Graphs}, author={Juho Hirvonen and Joel Rybicki and Stefan Schmid and Jukka Suomela}, journal={Electron. J. Comb.}, year={2014}, volume={24}, pages={4} }

We study the problem of finding large cuts in $d$-regular triangle-free graphs. In prior work, Shearer (1992) gives a randomised algorithm that finds a cut of expected size $(1/2 + 0.177/\sqrt{d})m$, where $m$ is the number of edges. We give a simpler algorithm that does much better: it finds a cut of expected size $(1/2 + 0.28125/\sqrt{d})m$. As a corollary, this shows that in any $d$-regular triangle-free graph there exists a cut of at least this size.
Our algorithm can be interpreted as a…

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