W. Haken (1971), Notes on Shimamoto’s Construction

Paper information

Title: Notes on Shimamoto’s Construction
Author: Wolfgang Haken
Source: Manuscript, October 20-24, 1971
4 Color Seminar
Received from: Wolfgang Haken, June 2018 by Professor Bertram Ludäscher, School of Information Sciences
Access provided by the Mathematics Library of the University of Illinois at Urbana-Champaign with the permission of Wolfgang Haken.
Available online: since August 2018

Table of Contents

• Definitions (abbreviated vocabulary)
• Kempe chain-argument and D-Reduction
• Statement of the main theorem
• Ancient theorems proving Theorem A₀
• Definition of S-, D-, E-graphs
• Statement of coloration theorems S and D
• Statement of coloration theorem S₂
• Statement of coloration theorem E
• Proof of Coloration theorem S
• Proof of coloration theorems (D.1)…(D.3)
• Proof of coloration theorems (D.4)…(D.7)
• Proof of (D.7) cont. and of (D.8)
• Figure illustrating the proof of (D.8)
• Proof of coloration theorem S₂
• Proof of coloration theorem (E.1)…(E.9)
• Proof of (E.9) cont. … (E.13)
• Proof of (E.13) cont. … (E.15)
• Statement of the Construction theorems
• Proof of Construction Theorems I, II
• Proof of construction theorem II, cont.
• Proof of construction theorem II, cont².
• Proof of Theorem A₁
• Proof of Theorems A₂ and A₃
• Proof of Theorem A