Add diagrams of the six witness Even Level Graphs and their bridge switches

Figure fig:n21-witnesses: each of the six Holton-McKay duals drawn as its
witness Even Level Graph in a radial-by-level layout (source centre,
level-k vertices on ring k), coloured by parity. Dashed red edges are the
flipped same-parity edges and solid green edges the introduced bridges;
applying the switches yields the dual. Duals 1,2 are ELGs outright.

draw_witnesses.py generates the combined 2x3 figure and per-dual PNGs from
the verified witness JSONs.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

papers/even_level_graph_generators/experiments/draw_witnesses.py

@@ -0,0 +1,113 @@
+"""Draw each of the six Holton-McKay duals as its witness Even Level Graph
+in a radial-by-level layout (source at centre, level-k vertices on ring k),
+coloured by parity, with the bridge switches highlighted: removed edges in
+red (dashed), added edges in green. Reads experiments/witnesses/dual_*.json.
+"""
+import sys
+import os
+import json
+import math
+sys.path.insert(0, '/Users/didericis/Code/math-research/papers/'
+                'level_resolutions_of_maximal_planar_graphs/experiments')
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+import networkx as nx
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+from matplotlib.lines import Line2D
+from test_conjecture import bfs_levels
+
+HERE = os.path.dirname(os.path.abspath(__file__))
+WDIR = os.path.join(HERE, 'witnesses')
+FDIR = os.path.join(HERE, '..', 'figures')
+
+EVEN_C = '#9ecae1'   # even-level vertices
+ODD_C = '#fdae6b'    # odd-level vertices
+
+
+def radial_pos(G, source):
+    levels = bfs_levels(G, frozenset({source}))
+    by_lvl = {}
+    for v, k in levels.items():
+        by_lvl.setdefault(k, []).append(v)
+    pos = {}
+    for k, verts in by_lvl.items():
+        verts = sorted(verts)
+        if k == 0:
+            pos[verts[0]] = (0.0, 0.0)
+            continue
+        m = len(verts)
+        for j, v in enumerate(verts):
+            ang = 2 * math.pi * j / m + (k * 0.6)
+            pos[v] = (k * math.cos(ang), k * math.sin(ang))
+    return pos, levels
+
+
+def draw(dual_index, ax):
+    data = json.load(open(os.path.join(WDIR, f'dual_{dual_index}.json')))
+    src = data['elg_source']
+    G = nx.Graph()
+    G.add_nodes_from(int(v) for v in data['labels'])
+    G.add_edges_from((a, b) for a, b in data['elg_edges'])
+    pos, levels = radial_pos(G, src)
+    colors = [EVEN_C if levels[v] % 2 == 0 else ODD_C for v in G.nodes()]
+
+    removed = {frozenset(s['remove']) for s in data['bridge_switches']}
+    added = [tuple(s['add']) for s in data['bridge_switches']]
+
+    plain = [e for e in G.edges() if frozenset(e) not in removed]
+    nx.draw_networkx_edges(G, pos, edgelist=plain, ax=ax,
+                           edge_color='#bdbdbd', width=0.8)
+    if removed:
+        nx.draw_networkx_edges(G, pos, edgelist=[tuple(e) for e in removed],
+                               ax=ax, edge_color='#d62728', width=2.2,
+                               style='dashed')
+    if added:
+        nx.draw_networkx_edges(nx.Graph(added), pos, edgelist=added, ax=ax,
+                               edge_color='#2ca02c', width=2.2)
+    nx.draw_networkx_nodes(G, pos, node_color=colors, node_size=210,
+                           edgecolors='#444444', linewidths=0.6, ax=ax)
+    nx.draw_networkx_labels(G, pos, font_size=7, ax=ax)
+    k = data['num_bridge_switches']
+    title = (f'dual {dual_index}: ELG (source {src})'
+             + (f'\n{k} bridge switch' + ('es' if k != 1 else '')
+                if k else '\n(Even Level Graph outright)'))
+    ax.set_title(title, fontsize=9)
+    ax.set_aspect('equal')
+    ax.axis('off')
+
+
+def main():
+    os.makedirs(FDIR, exist_ok=True)
+    # one combined 2x3 figure, plus individual files
+    fig, axes = plt.subplots(2, 3, figsize=(13, 9))
+    for i, ax in zip(range(6), axes.flat):
+        draw(i, ax)
+    legend = [
+        Line2D([0], [0], marker='o', color='w', markerfacecolor=EVEN_C,
+               markeredgecolor='#444', markersize=9, label='even level'),
+        Line2D([0], [0], marker='o', color='w', markerfacecolor=ODD_C,
+               markeredgecolor='#444', markersize=9, label='odd level'),
+        Line2D([0], [0], color='#d62728', lw=2.2, ls='dashed',
+               label='removed (flipped) edge'),
+        Line2D([0], [0], color='#2ca02c', lw=2.2, label='added (bridge) edge'),
+    ]
+    fig.legend(handles=legend, loc='lower center', ncol=4, fontsize=9,
+               frameon=False)
+    fig.tight_layout(rect=(0, 0.04, 1, 1))
+    out = os.path.join(FDIR, 'n21_witnesses.png')
+    fig.savefig(out, dpi=160)
+    print(f'wrote {out}')
+
+    for i in range(6):
+        f, a = plt.subplots(figsize=(5, 5))
+        draw(i, a)
+        f.tight_layout()
+        p = os.path.join(FDIR, f'n21_dual_{i}.png')
+        f.savefig(p, dpi=160)
+        plt.close(f)
+        print(f'wrote {p}')
+
+
+if __name__ == '__main__':
+    main()

papers/even_level_graph_generators/paper.tex

@@ -426,6 +426,19 @@ witnesses are step-verified.}
 \label{tab:n21}
 \end{table}
 
+\begin{figure}[ht]
+\centering
+\includegraphics[width=\textwidth]{figures/n21_witnesses.png}
+\caption{The witness Even Level Graph for each of the six Holton--McKay
+duals, drawn radially by level (source at the centre, level-$k$ vertices on
+ring $k$) and coloured by parity (blue even, orange odd). Dashed red edges
+are the same-parity edges flipped by the bridge switches; solid green edges
+are the bridge edges they introduce; applying the switches turns each Even
+Level Graph into the corresponding dual. Duals $1$ and $2$ are Even Level
+Graphs outright, so no switch is shown.}
+\label{fig:n21-witnesses}
+\end{figure}
+
 \begin{thebibliography}{9}
 
 \bibitem{holton-mckay}