didericis
7034f21ad8
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>
114 lines
4.2 KiB
Python
114 lines
4.2 KiB
Python
"""Draw each of the six Holton-McKay duals as its witness Even Level Graph
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in a radial-by-level layout (source at centre, level-k vertices on ring k),
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coloured by parity, with the bridge switches highlighted: removed edges in
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red (dashed), added edges in green. Reads experiments/witnesses/dual_*.json.
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"""
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import sys
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import os
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import json
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import math
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sys.path.insert(0, '/Users/didericis/Code/math-research/papers/'
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'level_resolutions_of_maximal_planar_graphs/experiments')
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sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
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import networkx as nx
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import matplotlib
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matplotlib.use('Agg')
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import matplotlib.pyplot as plt
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from matplotlib.lines import Line2D
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from test_conjecture import bfs_levels
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HERE = os.path.dirname(os.path.abspath(__file__))
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WDIR = os.path.join(HERE, 'witnesses')
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FDIR = os.path.join(HERE, '..', 'figures')
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EVEN_C = '#9ecae1' # even-level vertices
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ODD_C = '#fdae6b' # odd-level vertices
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def radial_pos(G, source):
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levels = bfs_levels(G, frozenset({source}))
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by_lvl = {}
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for v, k in levels.items():
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by_lvl.setdefault(k, []).append(v)
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pos = {}
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for k, verts in by_lvl.items():
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verts = sorted(verts)
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if k == 0:
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pos[verts[0]] = (0.0, 0.0)
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continue
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m = len(verts)
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for j, v in enumerate(verts):
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ang = 2 * math.pi * j / m + (k * 0.6)
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pos[v] = (k * math.cos(ang), k * math.sin(ang))
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return pos, levels
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def draw(dual_index, ax):
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data = json.load(open(os.path.join(WDIR, f'dual_{dual_index}.json')))
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src = data['elg_source']
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G = nx.Graph()
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G.add_nodes_from(int(v) for v in data['labels'])
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G.add_edges_from((a, b) for a, b in data['elg_edges'])
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pos, levels = radial_pos(G, src)
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colors = [EVEN_C if levels[v] % 2 == 0 else ODD_C for v in G.nodes()]
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removed = {frozenset(s['remove']) for s in data['bridge_switches']}
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added = [tuple(s['add']) for s in data['bridge_switches']]
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plain = [e for e in G.edges() if frozenset(e) not in removed]
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nx.draw_networkx_edges(G, pos, edgelist=plain, ax=ax,
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edge_color='#bdbdbd', width=0.8)
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if removed:
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nx.draw_networkx_edges(G, pos, edgelist=[tuple(e) for e in removed],
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ax=ax, edge_color='#d62728', width=2.2,
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style='dashed')
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if added:
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nx.draw_networkx_edges(nx.Graph(added), pos, edgelist=added, ax=ax,
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edge_color='#2ca02c', width=2.2)
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nx.draw_networkx_nodes(G, pos, node_color=colors, node_size=210,
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edgecolors='#444444', linewidths=0.6, ax=ax)
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nx.draw_networkx_labels(G, pos, font_size=7, ax=ax)
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k = data['num_bridge_switches']
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title = (f'dual {dual_index}: ELG (source {src})'
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+ (f'\n{k} bridge switch' + ('es' if k != 1 else '')
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if k else '\n(Even Level Graph outright)'))
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ax.set_title(title, fontsize=9)
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ax.set_aspect('equal')
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ax.axis('off')
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def main():
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os.makedirs(FDIR, exist_ok=True)
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# one combined 2x3 figure, plus individual files
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fig, axes = plt.subplots(2, 3, figsize=(13, 9))
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for i, ax in zip(range(6), axes.flat):
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draw(i, ax)
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legend = [
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Line2D([0], [0], marker='o', color='w', markerfacecolor=EVEN_C,
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markeredgecolor='#444', markersize=9, label='even level'),
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Line2D([0], [0], marker='o', color='w', markerfacecolor=ODD_C,
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markeredgecolor='#444', markersize=9, label='odd level'),
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Line2D([0], [0], color='#d62728', lw=2.2, ls='dashed',
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label='removed (flipped) edge'),
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Line2D([0], [0], color='#2ca02c', lw=2.2, label='added (bridge) edge'),
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]
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fig.legend(handles=legend, loc='lower center', ncol=4, fontsize=9,
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frameon=False)
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fig.tight_layout(rect=(0, 0.04, 1, 1))
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out = os.path.join(FDIR, 'n21_witnesses.png')
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fig.savefig(out, dpi=160)
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print(f'wrote {out}')
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for i in range(6):
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f, a = plt.subplots(figsize=(5, 5))
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draw(i, a)
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f.tight_layout()
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p = os.path.join(FDIR, f'n21_dual_{i}.png')
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f.savefig(p, dpi=160)
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plt.close(f)
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print(f'wrote {p}')
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if __name__ == '__main__':
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main()
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