Adds a worked example: G = C_8 with three non-crossing chords
{(v_0,v_2), (v_3,v_7), (v_4,v_6)}. Walks through the calculation
of P_e(G, 3) by propagating constraints:
1. Fix chord c_0 = a (3 choices).
2. Forces {c(e_0), c(e_7)} = {b, c} and {c(e_1), c(e_2)} = {b, c}
at v_0 and v_2; cycle constraint at v_1 ties them together.
3. Propagating to chord 3-7 forces c_3 = a and the adjacent
cycle edges to alternate {b, c}.
4. Propagating to chord 4-6 forces c_4 = a and cycle edges
continue the alternation.
Result: cycle edges alternate b, c around C_8 (OK since |C_8| is
even); all 3 chords get the same color a. Total proper 3-edge-
colorings: 3 (choice of a) × 2 (b/c assignment) = 6, verified by
Sage's chromatic-polynomial computation on L(G).
Note that the graph admits a UNIQUE proper 3-edge-coloring modulo
permutation of the 3 colors -- the chord structure forces all
three chords to take the "third" color absent on the polygon cycle.
Adds:
- draw_3chord_example.py
- fig_3chord_example.png
Paper grows from 4 to 5 pages.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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