K5-free graphs on n vertices with sublinear independence number lie at most (1/18 + o(1))n² edges from bipartiteness, and 1/18 is asymptotically best possible.
10 problems for partitions of triangle-free graphs.European Journal of Combinatorics, 121:103841, October 2024
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Bipartite cuts in Ramsey-Tur\'an style
K5-free graphs on n vertices with sublinear independence number lie at most (1/18 + o(1))n² edges from bipartiteness, and 1/18 is asymptotically best possible.