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Bounded chromatic number of graphs with small clique number and large minimum degree
We prove that every triangle-free graph with minimum degree at least $\frac{n}{3}$ is $4$-colorable and thereby settle a problem of Brandt and Thomassé (2005) at the threshold $\frac{n}{3}$. The number four is best possible. For a positive integer-valued function $f(n)=o(n)$, we relate the chromatic
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