didericis/math-research
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

even_level: extend conjecture test to the cyclically-5-connected case (n=24)

Browse Source 
Add the n=24 result to the Even Level Graph Generators paper: the dual of
the unique 44-vertex non-Hamiltonian cyclically-5-connected cubic planar
graph (Holton-McKay Fig. 2.10) -- a 24-vertex 5-connected triangulation,
the first conjecture test outside the 3-cut family -- is a bridge-derived
level graph, two verified bridge switches from an Even Level Graph
(source 19).

- Generate the graph rather than transcribe it: plantri -c5 lists all 6833
  5-connected 24-vertex triangulations; exactly one has a non-Hamiltonian
  dual, which also settles the uniqueness Holton-McKay left open at 44
  vertices (cyclically-5-connected triangulation <=> dual cubic graph).
- New abstract sentence + "cyclically-5-connected case: n=24" subsection,
  noting the classic 46-vertex Tutte graph is only cyclically 3-connected.
- Figure 6 (figures/fig210_dual.png): the dual T, parity-coloured, with the
  two introduced bridge edges {6,19} and {20,22} in green (style of Fig. 5).
- Experiments: test_fig210_dual_bridge.py (generate->filter->test pipeline),
  verify_fig210_witness.py (step-verifies the witness), draw_fig210_dual.py
  (figure), fig210_dual.g6 (the unique graph). paper.pdf rebuilt (10 pages).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-22 13:06:47 -04:00
parent 4693f63208
commit b45c3d5510
12 changed files with 657 additions and 59 deletions
Download Patch File Download Diff File Expand all files Collapse all files
papers/even_level_graph_generators/paper.log
+59 -33
View File
@@ -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 12:23
This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 22 MAY 2026 13:04
entering extended mode
restricted \write18 enabled.
%&-line parsing enabled.
@@ -354,58 +354,60 @@ File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv
e
))
[1{/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]
<fig_levels.png, id=56, 454.21695pt x 391.34206pt>
<fig_levels.png, id=59, 454.21695pt x 391.34206pt>
File: fig_levels.png Graphic file (type png)
<use fig_levels.png>
Package pdftex.def Info: fig_levels.png used on input line 184.
Package pdftex.def Info: fig_levels.png used on input line 189.
(pdftex.def) Requested size: 198.0011pt x 170.59666pt.
LaTeX Warning: `h' float specifier changed to `ht'.
<fig_level_cycle.png, id=58, 452.04884pt x 391.34206pt>
<fig_level_cycle.png, id=61, 452.04884pt x 391.34206pt>
File: fig_level_cycle.png Graphic file (type png)
<use fig_level_cycle.png>
Package pdftex.def Info: fig_level_cycle.png used on input line 198.
Package pdftex.def Info: fig_level_cycle.png used on input line 203.
(pdftex.def) Requested size: 198.0011pt x 171.40878pt.
LaTeX Warning: `h' float specifier changed to `ht'.
<fig_edge_switch.png, id=60, 859.65166pt x 378.33345pt>
<fig_edge_switch.png, id=63, 859.65166pt x 378.33345pt>
File: fig_edge_switch.png Graphic file (type png)
<use fig_edge_switch.png>
Package pdftex.def Info: fig_edge_switch.png used on input line 217.
Package pdftex.def Info: fig_edge_switch.png used on input line 222.
(pdftex.def) Requested size: 341.9989pt x 150.51671pt.
LaTeX Warning: `h' float specifier changed to `ht'.
<fig_parity_subgraph.png, id=62, 1076.46165pt x 319.79475pt>
<fig_parity_subgraph.png, id=65, 1076.46165pt x 319.79475pt>
File: fig_parity_subgraph.png Graphic file (type png)
<use fig_parity_subgraph.png>
Package pdftex.def Info: fig_parity_subgraph.png used on input line 235.
Package pdftex.def Info: fig_parity_subgraph.png used on input line 240.
(pdftex.def) Requested size: 360.0pt x 106.9477pt.
LaTeX Warning: `h' float specifier changed to `ht'.
[2] [3 <./fig_levels.png> <./fig_level_cycle.png>] [4 <./fig_edge_switch.png> <
./fig_parity_subgraph.png>]
[2] [3 <./fig_levels.png> <./fig_level_cycle.png>]
Underfull \vbox (badness 2277) has occurred while \output is active []
[4 <./fig_edge_switch.png> <./fig_parity_subgraph.png>]
Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref) removing `math shift' on input line 315.
(hyperref) removing `math shift' on input line 320.
Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref) removing `math shift' on input line 315.
(hyperref) removing `math shift' on input line 320.
Overfull \hbox (5.73714pt too wide) in paragraph at lines 327--331
Overfull \hbox (5.73714pt too wide) in paragraph at lines 332--336
\OT1/cmr/m/n/10 where $\OML/cmm/m/it/10 s\OT1/cmr/m/n/10 (\OML/cmm/m/it/10 G\OT
1/cmr/m/n/10 )$ is the num-ber of valid sources of $\OML/cmm/m/it/10 G$\OT1/cmr
/m/n/10 . The flag-rooting is the automorphism-
[]
Underfull \hbox (badness 1112) in paragraph at lines 354--354
Underfull \hbox (badness 1112) in paragraph at lines 359--359
\OT1/cmr/m/n/10 mor-phism; \OT1/cmr/m/it/10 flag-rooted ELGs \OT1/cmr/m/n/10 is
the automorphism-free count
[]
@@ -413,29 +415,52 @@ Underfull \hbox (badness 1112) in paragraph at lines 354--354
[5] [6]
Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref) removing `math shift' on input line 460.
(hyperref) removing `math shift' on input line 465.
Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref) removing `math shift' on input line 460.
(hyperref) removing `math shift' on input line 465.
<figures/n21_duals.png, id=119, 1373.13pt x 867.24pt>
<figures/n21_duals.png, id=123, 1373.13pt x 867.24pt>
File: figures/n21_duals.png Graphic file (type png)
<use figures/n21_duals.png>
Package pdftex.def Info: figures/n21_duals.png used on input line 520.
Package pdftex.def Info: figures/n21_duals.png used on input line 525.
(pdftex.def) Requested size: 360.0pt x 227.35617pt.
[7] [8 <./figures/n21_duals.png>] (./paper.aux)
Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref) removing `math shift' on input line 538.
Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref) removing `math shift' on input line 538.
Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref) removing `math shift' on input line 538.
Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref) removing `math shift' on input line 538.
[7] [8 <./figures/n21_duals.png>]
<figures/fig210_dual.png, id=138, 542.025pt x 542.025pt>
File: figures/fig210_dual.png Graphic file (type png)
<use figures/fig210_dual.png>
Package pdftex.def Info: figures/fig210_dual.png used on input line 587.
(pdftex.def) Requested size: 251.9989pt x 251.99767pt.
[9] [10 <./figures/fig210_dual.png>]
(./paper.aux)
Package rerunfilecheck Info: File `paper.out' has not changed.
(rerunfilecheck) Checksum: CF07A31709BA02BE3BA2BC89322768D0;1088.
(rerunfilecheck) Checksum: A0B582009EF9672D6DFFA8A6FC189E33;1351.
)
Here is how much of TeX's memory you used:
9758 strings out of 478268
151077 string characters out of 5846347
455062 words of memory out of 5000000
27656 multiletter control sequences out of 15000+600000
475666 words of font info for 53 fonts, out of 8000000 for 9000
9774 strings out of 478268
151348 string characters out of 5846347
455738 words of memory out of 5000000
27666 multiletter control sequences out of 15000+600000
475834 words of font info for 54 fonts, out of 8000000 for 9000
1302 hyphenation exceptions out of 8191
69i,9n,76p,781b,434s stack positions out of 10000i,1000n,20000p,200000b,200000s
69i,9n,76p,822b,533s stack positions out of 10000i,1000n,20000p,200000b,200000s
</usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb
></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmcsc10.pfb
></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmex10.pfb>
@@ -449,11 +474,12 @@ exlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/local/te
xlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy7.pfb></usr/local/texl
ive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb></usr/local/texli
ve/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmti8.pfb></usr/local/texlive
/2022/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb>
Output written on paper.pdf (8 pages, 1098280 bytes).
/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt10.pfb></usr/local/texlive/
2022/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb>
Output written on paper.pdf (10 pages, 1234426 bytes).
PDF statistics:
205 PDF objects out of 1000 (max. 8388607)
155 compressed objects within 2 object streams
38 named destinations out of 1000 (max. 500000)
82 words of extra memory for PDF output out of 10000 (max. 10000000)
226 PDF objects out of 1000 (max. 8388607)
170 compressed objects within 2 object streams
42 named destinations out of 1000 (max. 500000)
95 words of extra memory for PDF output out of 10000 (max. 10000000)