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Oct 4, 2023 at 4:29 comment added Alex Ravsky According to Theorem 7 from the above paper, for each $n\ge \mathbf 8$ there exists a doubly linear graph with $n$ vertices and $6n-20$ edges. When we partition this graph into two straight-edged planar graphs and triangulate each of them, we obtain two triangulations with at most $8$ common edges, which implies $f(n)\le 8$.
Oct 3, 2023 at 6:50 history bounty ended Till
Oct 2, 2023 at 18:45 history edited Tony Huynh CC BY-SA 4.0
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Oct 2, 2023 at 3:25 history edited Tony Huynh CC BY-SA 4.0
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Oct 2, 2023 at 3:19 history answered Tony Huynh CC BY-SA 4.0