Key points are not available for this paper at this time.
There are two particular ₆-graphs - the 6-cycle graphs with a diagonal. We find the planar Tur\'an number of each of them, i. e. the maximum number of edges in a planar graph G of n vertices not containing the given ₆ as a subgraph and we find infinitely many extremal constructions showing the sharpness of these results - apart from a small additive constant error in one of the cases.
Guan et al. (Thu,) studied this question.