Adds the concrete construction (40 vertices, 60 edges, cubic + planar
+ proper 3-edge-coloured) on which h_φ is simultaneously constant on
two Kempe cycles sharing an edge:
- K_{red, blue} = 8-cycle (the outer frame): all h_φ = -1
- K_{red, green} = 12-cycle (outer frame + upper-left ladder side):
all h_φ = -1
- They share the colour-red edge (0, 7) (and others).
The graph is drawn in TikZiT and stored as
papers/face_monochromatic_pairs/constant_heawood_counterexample.tikz
The Sage transcription + Heawood/Kempe verification + PNG renderer is
papers/face_monochromatic_pairs/experiments/counterexample_conj_5_5.py
Rendered PNG (with the four bent outer-face / trapezoid arcs matching
the tikz drawing) is at
papers/face_monochromatic_pairs/figures/no-two-constant-kempe-counterexample.png
Globally h_φ has 16 vertices at +1 and 24 at -1; the +1 vertices are
concentrated in the inner "tilted ladder" region, leaving the outer
and the K_{red,green}-extension all at -1. This is the structural
reason both Kempe cycles can be constant.
Also includes the TikZiT styles file default.tikzstyles defining the
red/blue/green edge styles used by the .tikz file.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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