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

Verify Remark 5.8 on genuine bite treads

Browse Source 
Bites arise when the inner outerplanar graph O has a bridge: the bridge
edge is traversed twice by the outer-face walk, so its medial vertex is
adjacent to four annular vertices.

- check_remark58_bite.py: a minimal bite tread (outer 4-cycle + interior
  bridge u-w) restricts to Kempe-balanced on all colourings (outer face).
- check_remark58_bite_rich.py: O = triangle abc + pendant bridge a-d gives
  one bite plus three singleton down teeth in the bite's inner-gap face;
  every restriction is Kempe-balanced (the three gap singletons are a
  rainbow in every global colouring).

Update Remark 5.8's verification note: the bite case, including singletons
in the bite-gap face, is now confirmed.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-06-11 16:46:53 -04:00
parent 5bed8b4dfb
commit cf035243f6
7 changed files with 286 additions and 36 deletions
Download Patch File Download Diff File Expand all files Collapse all files
papers/medial_tire_decompositions_of_plane_triangulations/paper.fdb_latexmk
+3 -3
View File
@@ -1,5 +1,5 @@
# Fdb version 3
["pdflatex"] 1781209574 "paper.tex" "paper.pdf" "paper" 1781209575
["pdflatex"] 1781210675 "paper.tex" "paper.pdf" "paper" 1781210676
"/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 ""
@@ -132,8 +132,8 @@
"/usr/local/texlive/2022/texmf-var/fonts/map/pdftex/updmap/pdftex.map" 1647878959 4410336 7d30a02e9fa9a16d7d1f8d037ba69641 ""
"/usr/local/texlive/2022/texmf-var/web2c/pdftex/pdflatex.fmt" 1665017617 2826443 7e98410c533054b636c6470db83a27bc ""
"/usr/local/texlive/2022/texmf.cnf" 1647878952 577 209b46be99c9075fd74d4c0369380e8c ""
"paper.aux" 1781209575 4206 a817291c83280f23be785ea9b9789717 "pdflatex"
"paper.tex" 1781209541 40737 e5d86b8964b20788119dc708cc9cd8ef ""
"paper.aux" 1781210676 4206 870862ca1c6762f39fd7ed9def109a09 "pdflatex"
"paper.tex" 1781210650 40922 403b0b9df57192dbf02362b0b06705c3 ""
(generated)
"paper.aux"
"paper.log"