Frame flip-asymmetry as first of further necessary properties

Adds a transitional section reframing the frequency results: the
relevant class is not all maximal planar graphs but those that resist
Kempe-style reductions, where flip-asymmetry's exclusion may have
real bite. Sets up subsequent development of additional necessary
properties of a minimum-order 5-chromatic counterexample.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

papers/flip_symmetric_maximal_planar_graphs/paper.tex

@@ -276,6 +276,19 @@ the minimum-degree-$5$ class --- which already contains every
 candidate minimum-order $5$-chromatic graph --- flip-symmetric
 examples become a vanishing fraction.
 
+\section{Further necessary properties of a minimal counterexample}
+
+The frequency data of Section~\ref{sec:frequency} look unflattering
+only when flip-symmetry is weighed against the full class of maximal
+planar graphs.  The class that actually matters --- minimum-order
+$5$-chromatic triangulations that also resist every Kempe-style
+reduction --- is far thinner, and flip-symmetry may exclude a
+substantially larger fraction of it if the configurations it removes
+overlap those responsible for Kempe reducibility.  We therefore turn
+to identifying further necessary properties of a minimum-order
+$5$-chromatic maximal planar graph, of which flip-asymmetry is the
+first.
+
 \end{document}
 
 %-----------------------------------------------------------------------