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.aux
+2 -2
View File
@@ -46,5 +46,5 @@
\newlabel{tocindent1}{17.77782pt}
\newlabel{tocindent2}{29.38873pt}
\newlabel{tocindent3}{0pt}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{10}{}\protected@file@percent }
\gdef \@abspage@last{10}
\@writefile{toc}{\contentsline {section}{\tocsection {}{}{References}}{11}{}\protected@file@percent }
\gdef \@abspage@last{11}