A. Mohapatra

An Improved Upper Bound for the Tur\'an Number of the Hexagon

For a graph $F$, the Tur\'an number $\operatorname{ex}(n,F)$ is the maximum number of edges in an $n$-vertex graph containing no copy of $F$. Determining the Tur\'an numbers of even cycles is a central problem in extremal graph theory and remains open in general. For $C_6$, the best previous upper bound was due to F\"u...