Replaces the spoke-only Figure 4 with a true barbell example:
Setup:
- B_out: hexagon u_0..u_5 (red).
- O = barbell: triangle {a_1, a_2, a_3} + triangle {b_1, b_2, b_3}
+ bridge a_3-b_1 (light red).
- 14 spokes triangulate the annulus into 14 annular triangles:
6 outer-cap + 6 inner-cap + 2 bridge-cap.
Dual placement is precise:
- All 14 blue dots at exact triangle centroids (via TikZ
barycentric cs).
- 13 edges of the Hamilton cycle wrap around the annulus
crossing each spoke.
- The bridge dual edge connects the two bridge-cap triangles
directly (dashed blue chord across the cycle).
Resulting Γ ≅ Θ(1, 7, 7): Hamilton cycle of length 14 with a
single length-1 chord. Outerplanar (the length-1 chord has no
internal degree-2 vertex, so no K_{2,3} minor).
This now properly demonstrates the chord arising from a real
bridge, exactly as the theorem and Remark 1.14 describe.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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