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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