The Wechsler conjecture would show f(9)>=6 should be achievable by connecting 6 triangles via shared vertices in a K33 connection pattern (each red triangle shares each vertex with exactly 1 blue triangle). However, I doubt it. I think this configuration cannot be realized and if so the Wechsler conjecture is disproven. On the bright side, every time you find another unrealizable configuration, you can add that as a new excluded subgraph making the combinatorial upper bound get tighter. [Also, by using Petersen graph instead of K33 we would find f(15)>=10.
From Heawood graph we would find f(21)>=14. From Tutte-Coxeter graph would follow f(45)>=30. Some of these might even be true.]
Perhaps relevant: This paper by LA Szekely http://www.cs.umd.edu/~gasarch/erdos_dist/szekely.pdf proves that a V-vertex graph drawn in the plane with line segment edges, each of length=1, has at most O(V^(4/3)) edges. I think (have not checked carefully!) his proof also is valid for graphs drawn on surface of a sphere using geodesic segment edges. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)