The maximum number of edges in 1-planar graphs avoiding certain subgraphs
- The maximum number of edges in a
$C_3$ -free$1$ -planar graph:$3(n-O(1))$ - the maximum number of edges in a
$C_4$ -free$1$ -planar graph:$\tfrac{7}{3}(n-O(1))$ - the maximum number of edges in a planar graph of girth at least
$5$ (?)