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Large Cuts with Local Algorithms on Triangle-Free Graphs
2017
Electronic Journal of Combinatorics
Let $G$ be a $d$-regular triangle-free graph with $m$ edges. We present an algorithm which finds a cut in $G$ with at least $(1/2 + 0.28125/\sqrt{d})m$ edges in expectation, improving upon Shearer's classic result. In particular, this implies that any $d$-regular triangle-free graph has a cut of at least this size, and thus, we obtain a new lower bound for the maximum number of edges in a bipartite subgraph of $G$.Our algorithm is simpler than Shearer's classic algorithm and it can be
doi:10.37236/6862
fatcat:3n722m5z4rgavbpnmmog7fkriq