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/dβ)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/dβ)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 very efficient randomised distributed
algorithm: each node needs to produce only one random bit, and the algorithm
runs in one synchronous communication round. This work is also a case study of
applying computational techniques in the design of distributed algorithms: our
algorithm was designed by a computer program that searched for optimal
algorithms for small values of d.Comment: 1+17 pages, 8 figure