Add Kempe-balanced colouring definition and validity classifier

Define Kempe-balanced colourings of a full medial tire graph (Def 5.7):
for each valid face (outer face or interior non-tooth face of B(T)) and
each colour pair {a,b}, the number of tooth apexes incident to the face
coloured a or b must be even.  Add Remark 5.8 (necessity: a colouring of
M(T) extends to M(G) only if it is Kempe-balanced) and rename Lemma 5.5
to "Kempe chains are cycles".

Add kempe_valid_colorings.py: enumerate all proper 3-colourings of a full
medial tire graph, label each Kempe-balanced/valid or invalid, and plot
them with the offending face's Kempe chains and odd apex set highlighted
on invalid panels.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

papers/medial_tire_decompositions_of_plane_triangulations/paper.aux

@@ -35,6 +35,10 @@
 \newlabel{conj:medial-chain-pigeonhole}{{5.2}{7}}
 \newlabel{conj:medial-route-fct}{{5.3}{7}}
 \@writefile{toc}{\contentsline {subsection}{\tocsubsection {}{5.1}{Kempe-cycle conservation across medial tires}}{7}{}\protected@file@percent }
+\newlabel{lem:kempe-cycles}{{5.5}{7}}
+\newlabel{lem:kempe-conservation}{{5.6}{8}}
+\newlabel{def:kempe-balanced}{{5.7}{8}}
+\newlabel{rem:kempe-balance-necessary}{{5.8}{8}}
 \bibcite{bauerfeld-nested-tire-decompositions}{1}
 \bibcite{tait-original}{2}
 \newlabel{tocindent-1}{0pt}