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

Add Even Level Graph Generators paper + extend Level Switching reachability

Browse Source 
- New paper papers/even_level_graph_generators/: defines Even Level
  Graph (every level cycle even), derived level graphs, intertwining
  trees, and the disjunction conjecture (every maximal planar graph is
  a derived level graph or intertwining tree). Empirically tested
  through n=11: every iso class is at least an intertwining tree, so
  the disjunction holds trivially in this range. The intertwining tree
  disjunct fails at the Tutte graph dual (n=25), so the disjunction
  becomes non-trivial past some unknown threshold.

- Level Switching paper: adds Section 4 (Reachability via edge
  switches) with the two-step argument (Sleator-Tarjan-Thurston for
  Case 1; face-merges for Case 2) and Theorem 4.1 (O(n) edge switches
  suffice to reach all-depth-0).

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-21 16:44:39 -04:00
parent 082ee31966
commit c947ce75ff
29 changed files with 2180 additions and 23 deletions
Download Patch File Download Diff File Expand all files Collapse all files
papers/level_switching/paper.log
+30 -21
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) 20 MAY 2026 23:18
This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 21 MAY 2026 14:28
entering extended mode
restricted \write18 enabled.
%&-line parsing enabled.
@@ -353,12 +353,12 @@ Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4
File: epstopdf-sys.cfg 2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Liv
e
))
<fig_level_source.png, id=32, 715.11165pt x 317.988pt>
<fig_level_source.png, id=56, 715.11165pt x 317.988pt>
File: fig_level_source.png Graphic file (type png)
<use fig_level_source.png>
Package pdftex.def Info: fig_level_source.png used on input line 105.
(pdftex.def) Requested size: 306.0022pt x 136.07228pt.
<fig_levels.png, id=34, 454.21695pt x 391.34206pt>
<fig_levels.png, id=58, 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 122.
@@ -367,7 +367,7 @@ Package pdftex.def Info: fig_levels.png used on input line 122.
LaTeX Warning: `h' float specifier changed to `ht'.
<fig_level_cycle.png, id=35, 452.04884pt x 391.34206pt>
<fig_level_cycle.png, id=59, 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 136.
@@ -377,7 +377,7 @@ LaTeX Warning: `h' float specifier changed to `ht'.
[1{/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map} <./fig
_level_source.png>]
<fig_edge_switch.png, id=57, 859.65166pt x 378.33345pt>
<fig_edge_switch.png, id=81, 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 155.
@@ -386,7 +386,7 @@ Package pdftex.def Info: fig_edge_switch.png used on input line 155.
LaTeX Warning: `h' float specifier changed to `ht'.
<fig_parity_subgraph.png, id=59, 1076.46165pt x 319.79475pt>
<fig_parity_subgraph.png, id=83, 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 173.
@@ -395,7 +395,7 @@ Package pdftex.def Info: fig_parity_subgraph.png used on input line 173.
LaTeX Warning: `h' float specifier changed to `ht'.
[2 <./fig_levels.png> <./fig_level_cycle.png>]
<fig_facial_depth.png, id=72, 482.40225pt x 498.663pt>
<fig_facial_depth.png, id=96, 482.40225pt x 498.663pt>
File: fig_facial_depth.png Graphic file (type png)
<use fig_facial_depth.png>
Package pdftex.def Info: fig_facial_depth.png used on input line 200.
@@ -413,7 +413,7 @@ bal-anced-ness gives $[](\OML/cmm/m/it/10 A[]\OT1/cmr/m/n/10 ) = \OML/cmm/m/it/
/m/n/10 ) \OMS/cmsy/m/n/10 ^^T
[]
<fig_no_balanced_switch.png, id=107, 483.0045pt x 498.2615pt>
<fig_no_balanced_switch.png, id=131, 483.0045pt x 498.2615pt>
File: fig_no_balanced_switch.png Graphic file (type png)
<use fig_no_balanced_switch.png>
Package pdftex.def Info: fig_no_balanced_switch.png used on input line 395.
@@ -421,7 +421,7 @@ Package pdftex.def Info: fig_no_balanced_switch.png used on input line 395.
LaTeX Warning: `h' float specifier changed to `ht'.
<fig_preprocessing.png, id=110, 998.932pt x 513.5185pt>
<fig_preprocessing.png, id=134, 998.932pt x 513.5185pt>
File: fig_preprocessing.png Graphic file (type png)
<use fig_preprocessing.png>
Package pdftex.def Info: fig_preprocessing.png used on input line 426.
@@ -462,7 +462,7 @@ cmm/m/it/10 ; \OT1/cmr/m/n/10 14)\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 (17\OML/cmm
/m/it/10 ; \OT1/cmr/m/n/10 19\OML/cmm/m/it/10 ; \OT1/cmr/m/n/10 0)$
[]
<fig_d2_recursive.png, id=128, 1293.633pt x 447.64888pt>
<fig_d2_recursive.png, id=152, 1293.633pt x 447.64888pt>
File: fig_d2_recursive.png Graphic file (type png)
<use fig_d2_recursive.png>
Package pdftex.def Info: fig_d2_recursive.png used on input line 477.
@@ -472,15 +472,24 @@ Overfull \hbox (44.02832pt too wide) detected at line 496
[][]
[]
[8 <./fig_d2_recursive.png>] [9] (./paper.aux)
[8 <./fig_d2_recursive.png>] [9]
Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref) removing `math shift' on input line 581.
Package hyperref Warning: Token not allowed in a PDF string (Unicode):
(hyperref) removing `math shift' on input line 581.
[10] [11] (./paper.aux)
Package rerunfilecheck Info: File `paper.out' has not changed.
(rerunfilecheck) Checksum: DB53A88C1A1F5BD90EDB1F1E02E41C38;1447.
(rerunfilecheck) Checksum: EB616E34045D97804AC077E984931199;2673.
)
Here is how much of TeX's memory you used:
9791 strings out of 478268
151840 string characters out of 5846347
458685 words of memory out of 5000000
27682 multiletter control sequences out of 15000+600000
9811 strings out of 478268
152095 string characters out of 5846347
458816 words of memory out of 5000000
27691 multiletter control sequences out of 15000+600000
475666 words of font info for 53 fonts, out of 8000000 for 9000
1302 hyphenation exceptions out of 8191
69i,9n,76p,781b,448s stack positions out of 10000i,1000n,20000p,200000b,200000s
@@ -498,10 +507,10 @@ 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 (9 pages, 1268281 bytes).
Output written on paper.pdf (11 pages, 1286221 bytes).
PDF statistics:
215 PDF objects out of 1000 (max. 8388607)
156 compressed objects within 2 object streams
42 named destinations out of 1000 (max. 500000)
102 words of extra memory for PDF output out of 10000 (max. 10000000)
259 PDF objects out of 1000 (max. 8388607)
198 compressed objects within 2 object streams
53 named destinations out of 1000 (max. 500000)
150 words of extra memory for PDF output out of 10000 (max. 10000000)