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didericis afe4bf4859 coloring_nested_tire_graphs: define inner and outer spokes (Def 1.17)
Adds a new definition partitioning V(T'_{f'}) \ V(f') by geometric
location relative to the face f':

  V_out(T'_{f'}) := { v in V(T'_{f'}) \ V(f') : v lies outside the
                      closure of f' }
                 = "outer spokes"

  V_in(T'_{f'})  := { v in V(T'_{f'}) \ V(f') : v lies inside the
                      open region f' }
                 = "inner spokes"

These are well-defined because the boundary walk of f' is V(f') by
definition, so no element of V(T'_{f'}) \ V(f') sits on ∂f'.

In the spoke-only setting (T'_ann = C_{n+m}), the inner spokes of
the inner face are the O-side non-annular dual vertices and the
outer spokes are the source-side non-annular dual vertices (and
vice-versa for the outer face).

Paper stays at 10 pages.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
2026-05-25 23:14:58 -04:00
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