didericis
53a676971c
Adds Definition (cut tire) to cut_depth_label.tex:
Given the depth labelling on G'_i, for each d > 0 let H_d be the
subgraph on depth-d edges (with inherited planar embedding). For
each face f of H_d, the cut tire at (d, f) is the subgraph of G'_i
consisting of:
- every edge on the boundary walk of f (all depth d), and
- every edge of G'_i incident to the boundary walk of f with
depth d-1 or d+1.
The depth-d edges form the "face boundary"; the d-1 edges are
"inner spokes" (toward the cut); the d+1 edges are "outer spokes."
This is the dual-side analogue of the tire annular face connector
T'_{f'} (paper.tex Def. 1.16):
face boundary ↔ T'_ann (annular subgraph at depth d)
cut tire ↔ T'_{f'} (annular face connector)
inner/outer spokes ↔ inner/outer spokes of T'_{f'}
Adds experiments/cut_tire.py producing fig_cut_tire.png:
5-panel visualisation of cut tires at depths d = 1, 2, 4, 5, 6 on
G'_1 (V\S half of Holton-McKay #0). Outermost tire at d=1 (face
length 12, 5+4 spokes); innermost at d=6 (face length 12, 7+1).
Note grows from 3 → 5 pages.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>