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Add Kempe-chain structure of 4-colorings of edge-deletion subgraphs

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For G_0 a minimum-order 5-chromatic maximal planar graph and any
4-coloring of G_0 - uv, the endpoints u, v must share a color, and the
color classes pairing that color with each of two other colors must
each induce a u-v path. The Kempe-chain parts follow from a standard
swap-on-component contradiction against the shared-color claim.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
This commit is contained in:
didericis
2026-05-14 00:31:40 -04:00
parent f6144b98b5
commit 6c7bd9e0db
5 changed files with 42 additions and 9 deletions
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papers/flip_symmetric_maximal_planar_graphs/paper.log
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This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022) (preloaded format=pdflatex 2022.10.5) 14 MAY 2026 00:30
entering extended mode
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[2] [3] [4] (./paper.aux) )
Here is how much of TeX's memory you used:
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13156 strings out of 478268
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@@ -526,7 +526,7 @@ mti10.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cm
ti8.pfb></usr/local/texlive/2022/texmf-dist/fonts/type1/public/amsfonts/cm/cmtt
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msam10.pfb>
Output written on paper.pdf (4 pages, 186074 bytes).
Output written on paper.pdf (4 pages, 189743 bytes).
PDF statistics:
90 PDF objects out of 1000 (max. 8388607)
55 compressed objects within 1 object stream