From b3998fbdb307a753130a5f04d4dca0539f79f217 Mon Sep 17 00:00:00 2001 From: didericis Date: Fri, 22 May 2026 11:23:36 -0400 Subject: [PATCH] Redraw n=21 witness figures as crossing-free planar graphs Replace the radial (crossing-heavy) figure with two crossing-free planar drawings (networkx planar_layout / Chrobak-Payne): fig:n21-elgs -- the six witness Even Level Graphs, parity-coloured, with the bridge-switch-flipped edges dashed red; fig:n21-duals -- the six resulting duals, with the introduced bridge edges solid green. ELG and dual are drawn with independent planar layouts so neither has any edge crossing (a flip diagonal would otherwise cross other edges when its quadrilateral is non-convex, which happens for duals 0 and 3). Drop forced equal aspect so panels fill and labels separate. Co-Authored-By: Claude Opus 4.7 --- .../experiments/draw_witnesses.py | 155 +++++++++--------- .../figures/n21_dual_0.png | Bin 126609 -> 0 bytes .../figures/n21_dual_1.png | Bin 99994 -> 0 bytes .../figures/n21_dual_2.png | Bin 98842 -> 0 bytes .../figures/n21_dual_3.png | Bin 128835 -> 0 bytes .../figures/n21_dual_4.png | Bin 137986 -> 0 bytes .../figures/n21_dual_5.png | Bin 138058 -> 0 bytes .../figures/n21_duals.png | Bin 0 -> 667947 bytes .../figures/n21_elgs.png | Bin 0 -> 679343 bytes .../figures/n21_witnesses.png | Bin 649971 -> 0 bytes papers/even_level_graph_generators/paper.aux | 8 +- .../paper.fdb_latexmk | 11 +- papers/even_level_graph_generators/paper.fls | 5 + papers/even_level_graph_generators/paper.log | 35 ++-- papers/even_level_graph_generators/paper.pdf | Bin 1048542 -> 1620175 bytes papers/even_level_graph_generators/paper.tex | 29 +++- 16 files changed, 140 insertions(+), 103 deletions(-) delete mode 100644 papers/even_level_graph_generators/figures/n21_dual_0.png delete mode 100644 papers/even_level_graph_generators/figures/n21_dual_1.png delete mode 100644 papers/even_level_graph_generators/figures/n21_dual_2.png delete mode 100644 papers/even_level_graph_generators/figures/n21_dual_3.png delete mode 100644 papers/even_level_graph_generators/figures/n21_dual_4.png delete mode 100644 papers/even_level_graph_generators/figures/n21_dual_5.png create mode 100644 papers/even_level_graph_generators/figures/n21_duals.png create mode 100644 papers/even_level_graph_generators/figures/n21_elgs.png delete mode 100644 papers/even_level_graph_generators/figures/n21_witnesses.png diff --git a/papers/even_level_graph_generators/experiments/draw_witnesses.py b/papers/even_level_graph_generators/experiments/draw_witnesses.py index 7e8d86d..afd9216 100644 --- a/papers/even_level_graph_generators/experiments/draw_witnesses.py +++ b/papers/even_level_graph_generators/experiments/draw_witnesses.py @@ -1,12 +1,16 @@ -"""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. +"""Draw the six Holton-McKay duals and their witness Even Level Graphs as +crossing-free planar drawings (networkx planar_layout, Chrobak-Payne). +Two figures: + n21_elgs.png -- the six witness Even Level Graphs, parity-coloured, + with the edges flipped by the bridge switches dashed red; + n21_duals.png -- the six resulting duals, parity-coloured (same fixed + parity labelling), with the introduced bridge edges green. +Reads experiments/witnesses/dual_*.json. ELG and dual are drawn with +independent planar layouts so neither has any edge crossing. """ 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__))) @@ -15,98 +19,95 @@ 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 +EVEN_C = '#9ecae1' # even-parity vertices +ODD_C = '#fdae6b' # odd-parity 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 load(i): + return json.load(open(os.path.join(WDIR, f'dual_{i}.json'))) -def draw(dual_index, ax): - data = json.load(open(os.path.join(WDIR, f'dual_{dual_index}.json'))) - src = data['elg_source'] +def graph_of(edges, labels): 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()] + G.add_nodes_from(int(v) for v in labels) + G.add_edges_from((a, b) for a, b in edges) + return G - 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] +def draw(ax, G, labels, highlight, hcolor, hstyle, title): + pos = nx.planar_layout(G) + colors = [EVEN_C if labels[str(v)] == 0 else ODD_C for v in G.nodes()] + hl = {frozenset(e) for e in highlight} + plain = [e for e in G.edges() if frozenset(e) not in hl] 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, + edge_color='#b0b0b0', width=0.8) + if hl: + nx.draw_networkx_edges(G, pos, edgelist=[tuple(e) for e in hl], ax=ax, + edge_color=hcolor, width=2.4, style=hstyle) + nx.draw_networkx_nodes(G, pos, node_color=colors, node_size=200, 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') + nx.draw_networkx_labels(G, pos, font_size=8, ax=ax) + ax.set_title(title, fontsize=10) + ax.margins(0.12) ax.axis('off') +def legend(fig, kind): + handles = [ + Line2D([0], [0], marker='o', color='w', markerfacecolor=EVEN_C, + markeredgecolor='#444', markersize=9, label='even parity'), + Line2D([0], [0], marker='o', color='w', markerfacecolor=ODD_C, + markeredgecolor='#444', markersize=9, label='odd parity'), + ] + if kind == 'elg': + handles.append(Line2D([0], [0], color='#d62728', lw=2.4, ls='dashed', + label='edge flipped by a bridge switch')) + else: + handles.append(Line2D([0], [0], color='#2ca02c', lw=2.4, + label='bridge edge introduced')) + fig.legend(handles=handles, loc='lower center', ncol=3, fontsize=9, + frameon=False) + + 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}') + # Figure 1: the six witness Even Level Graphs (flipped edges red dashed) + fig, axes = plt.subplots(2, 3, figsize=(19, 12)) + for i, ax in zip(range(6), axes.flat): + d = load(i) + G = graph_of(d['elg_edges'], d['labels']) + removed = [s['remove'] for s in d['bridge_switches']] + k = d['num_bridge_switches'] + sub = (f"{k} bridge switch" + ("es" if k != 1 else "") + if k else "Even Level Graph outright") + draw(ax, G, d['labels'], removed, '#d62728', 'dashed', + f"dual {i}: ELG (source {d['elg_source']})\n{sub}") + legend(fig, 'elg') + fig.tight_layout(rect=(0, 0.04, 1, 1)) + p1 = os.path.join(FDIR, 'n21_elgs.png') + fig.savefig(p1, dpi=160) + plt.close(fig) + print(f'wrote {p1}') + + # Figure 2: the six resulting duals (introduced bridge edges green) + fig, axes = plt.subplots(2, 3, figsize=(19, 12)) + for i, ax in zip(range(6), axes.flat): + d = load(i) + G = graph_of(d['dual_edges'], d['labels']) + added = [s['add'] for s in d['bridge_switches']] + draw(ax, G, d['labels'], added, '#2ca02c', 'solid', f"dual {i}") + 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{1}{\ignorespaces The six Holton--McKay duals at $n = 21$, the first triangulations that are not intertwining trees. Each is a bridge-derived level graph: duals $1$ and $2$ are Even Level Graphs outright (zero switches), and the remaining four reach an Even Level Graph in $1$--$4$ bridge switches. All witnesses are step-verified.}}{6}{table.1}\protected@file@percent } +\newlabel{tab:n21}{{1}{6}{The six Holton--McKay duals at $n = 21$, the first triangulations that are not intertwining trees. Each is a bridge-derived level graph: duals $1$ and $2$ are Even Level Graphs outright (zero switches), and the remaining four reach an Even Level Graph in $1$--$4$ bridge switches. All witnesses are step-verified}{table.1}{}} \@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{6}{section*.3}\protected@file@percent } -\gdef \@abspage@last{6} +\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces The witness Even Level Graph for each of the six Holton--McKay duals, drawn as a crossing-free planar graph and coloured by parity (blue even, orange odd, with respect to the fixed level-parity labelling). The dashed red edges are the same-parity edges that the bridge switches flip; flipping them yields the corresponding dual in Figure\nonbreakingspace \ref {fig:n21-duals}. Duals $1$ and $2$ are Even Level Graphs outright, so no edge is flipped.}}{7}{figure.5}\protected@file@percent } +\newlabel{fig:n21-elgs}{{5}{7}{The witness Even Level Graph for each of the six Holton--McKay duals, drawn as a crossing-free planar graph and coloured by parity (blue even, orange odd, with respect to the fixed level-parity labelling). The dashed red edges are the same-parity edges that the bridge switches flip; flipping them yields the corresponding dual in Figure~\ref {fig:n21-duals}. Duals $1$ and $2$ are Even Level Graphs outright, so no edge is flipped}{figure.5}{}} +\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces The six Holton--McKay duals, drawn as crossing-free planar graphs with the same parity colouring. The solid green edges are the bridge edges introduced by the switches from the Even Level Graphs of Figure\nonbreakingspace \ref {fig:n21-elgs}. Each green edge is a bridge of its parity subgraph, so no new cycle -- and in particular no odd cycle -- is created; duals $1$ and $2$ coincide with their Even Level Graphs and have no added edge.}}{8}{figure.6}\protected@file@percent } +\newlabel{fig:n21-duals}{{6}{8}{The six Holton--McKay duals, drawn as crossing-free planar graphs with the same parity colouring. The solid green edges are the bridge edges introduced by the switches from the Even Level Graphs of Figure~\ref {fig:n21-elgs}. Each green edge is a bridge of its parity subgraph, so no new cycle -- and in particular no odd cycle -- is created; duals $1$ and $2$ coincide with their Even Level Graphs and have no added edge}{figure.6}{}} +\gdef \@abspage@last{8} diff --git a/papers/even_level_graph_generators/paper.fdb_latexmk b/papers/even_level_graph_generators/paper.fdb_latexmk index 80040e0..f55db98 100644 --- a/papers/even_level_graph_generators/paper.fdb_latexmk +++ b/papers/even_level_graph_generators/paper.fdb_latexmk @@ -1,6 +1,6 @@ # Fdb version 3 -["pdflatex"] 1779461873 "/Users/didericis/Code/math-research/papers/even_level_graph_generators/paper.tex" "paper.pdf" "paper" 1779461874 - "/Users/didericis/Code/math-research/papers/even_level_graph_generators/paper.tex" 1779461873 15887 19952eaaf0fc5ca355be18e4eff4aaed "" +["pdflatex"] 1779463291 "/Users/didericis/Code/math-research/papers/even_level_graph_generators/paper.tex" "paper.pdf" "paper" 1779463293 + "/Users/didericis/Code/math-research/papers/even_level_graph_generators/paper.tex" 1779463291 18288 7a31bbe6e6a18516ee92fc4bff904881 "" "/usr/local/texlive/2022/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1246382020 1004 54797486969f23fa377b128694d548df "" "/usr/local/texlive/2022/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1246382020 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 "" @@ -90,9 +90,10 @@ "fig_level_cycle.png" 1779389598 83736 ee54074ab1383a0dcc7fc20387e34bdc "" "fig_levels.png" 1779389598 88029 5564f46c0a183f3777727b651e7dc461 "" "fig_parity_subgraph.png" 1779389598 191771 f069aa94c8f49b3c7fd9c71426feff2d "" - "paper.aux" 1779461874 5767 d6f46d8ee667b35ce0393ad310fffd64 "pdflatex" - "paper.out" 1779461874 1047 aeccb746cf11915bcb68f1e7ff8075a7 "pdflatex" - "paper.tex" 1779461873 15887 19952eaaf0fc5ca355be18e4eff4aaed "" + "figures/n21_witnesses.png" 1779463145 347960 9cff26f0427b981c675f214ca5cc1513 "" + "paper.aux" 1779463292 7658 3054ab5e5e2c2d6239a5f60f25708981 "pdflatex" + "paper.out" 1779463292 1047 aeccb746cf11915bcb68f1e7ff8075a7 "pdflatex" + "paper.tex" 1779463291 18288 7a31bbe6e6a18516ee92fc4bff904881 "" (generated) "paper.aux" "paper.log" diff --git a/papers/even_level_graph_generators/paper.fls b/papers/even_level_graph_generators/paper.fls index 9e0094d..46df0fc 100644 --- a/papers/even_level_graph_generators/paper.fls +++ b/papers/even_level_graph_generators/paper.fls @@ -566,6 +566,11 @@ INPUT ./fig_parity_subgraph.png INPUT fig_parity_subgraph.png INPUT ./fig_parity_subgraph.png INPUT ./fig_parity_subgraph.png +INPUT ./figures/n21_witnesses.png +INPUT ./figures/n21_witnesses.png +INPUT figures/n21_witnesses.png +INPUT ./figures/n21_witnesses.png +INPUT ./figures/n21_witnesses.png INPUT paper.aux INPUT ./paper.out INPUT ./paper.out diff --git a/papers/even_level_graph_generators/paper.log b/papers/even_level_graph_generators/paper.log index a9369cd..350a52c 100644 --- a/papers/even_level_graph_generators/paper.log +++ b/papers/even_level_graph_generators/paper.log @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 22 MAY 2026 11:11 +This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 22 MAY 2026 11:23 entering extended mode restricted \write18 enabled. %&-line parsing enabled. @@ -393,18 +393,29 @@ Package hyperref Warning: Token not allowed in a PDF string (Unicode): Package hyperref Warning: Token not allowed in a PDF string (Unicode): (hyperref) removing `math shift' on input line 371. -[5] [6] (./paper.aux) +[5] + +File: figures/n21_elgs.png Graphic file (type png) + +Package pdftex.def Info: figures/n21_elgs.png used on input line 431. +(pdftex.def) Requested size: 360.0pt x 227.35617pt. + +File: figures/n21_duals.png Graphic file (type png) + +Package pdftex.def Info: figures/n21_duals.png used on input line 444. +(pdftex.def) Requested size: 360.0pt x 227.35617pt. + [6] [7 <./figures/n21_elgs.png>] [8 <./figures/n21_duals.png>] (./paper.aux) Package rerunfilecheck Info: File `paper.out' has not changed. 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a/papers/even_level_graph_generators/paper.tex +++ b/papers/even_level_graph_generators/paper.tex @@ -428,15 +428,28 @@ witnesses are step-verified.} \begin{figure}[ht] \centering -\includegraphics[width=\textwidth]{figures/n21_witnesses.png} +\includegraphics[width=\textwidth]{figures/n21_elgs.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} +duals, drawn as a crossing-free planar graph and coloured by parity (blue +even, orange odd, with respect to the fixed level-parity labelling). The +dashed red edges are the same-parity edges that the bridge switches flip; +flipping them yields the corresponding dual in +Figure~\ref{fig:n21-duals}. Duals $1$ and $2$ are Even Level Graphs +outright, so no edge is flipped.} +\label{fig:n21-elgs} +\end{figure} + +\begin{figure}[ht] +\centering +\includegraphics[width=\textwidth]{figures/n21_duals.png} +\caption{The six Holton--McKay duals, drawn as crossing-free planar graphs +with the same parity colouring. The solid green edges are the bridge edges +introduced by the switches from the Even Level Graphs of +Figure~\ref{fig:n21-elgs}. Each green edge is a bridge of its parity +subgraph, so no new cycle -- and in particular no odd cycle -- is created; +duals $1$ and $2$ coincide with their Even Level Graphs and have no added +edge.} +\label{fig:n21-duals} \end{figure} \begin{thebibliography}{9}

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