{"id":2092,"date":"2018-08-17T18:49:34","date_gmt":"2018-08-17T18:49:34","guid":{"rendered":"http:\/\/wordpress.library.illinois.edu\/mtx\/?page_id=2092"},"modified":"2018-08-24T18:49:26","modified_gmt":"2018-08-24T18:49:26","slug":"w-haken-1971-notes-on-shimamotos-construction","status":"publish","type":"page","link":"https:\/\/wordpress.library.illinois.edu\/mtx\/w-haken-1971-notes-on-shimamotos-construction\/","title":{"rendered":"W. Haken (1971), Notes on Shimamoto\u2019s Construction"},"content":{"rendered":"<p><strong><\/p>\n<h3>Paper information<\/h3>\n<p><\/strong><\/p>\n<p><strong>Title:<\/strong> Notes on Shimamoto\u2019s Construction<br \/>\n<strong>Author:<\/strong> Wolfgang Haken<br \/>\n<strong>Source:<\/strong> Manuscript, October 20-24, 1971<br \/>\n4 Color Seminar<br \/>\n<strong>Received from:<\/strong> Wolfgang Haken, June 2018 by <a href=\"https:\/\/ischool.illinois.edu\/people\/bertram-ludascher\">Professor Bertram Lud\u00e4scher<\/a>, School of Information Sciences<br \/>\nAccess provided by the <a href=\"http:\/\/www.library.illinois.edu\/mtx\/\">Mathematics Library<\/a> of the University of Illinois at Urbana-Champaign with the permission of Wolfgang Haken.<br \/>\n<strong>Available online:<\/strong> since August 2018<\/p>\n<h3><strong><\/p>\n<p align=\"center\">Table of Contents<\/strong><\/h3>\n<\/p>\n<ul>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=1\">Definitions (abbreviated vocabulary)<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=2\">Kempe chain-argument and D-Reduction<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=3\">Statement of the main theorem<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=4\">Ancient theorems proving Theorem A<sub>0<\/sub><\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=7\">Definition of S-, D-, E-graphs<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=8\">Statement of coloration theorems S and D<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=9\">Statement of coloration theorem S<sub>2<\/sub><\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=10\">Statement of coloration theorem E<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=11\">Proof of Coloration theorem S<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=12\">Proof of coloration theorems (D.1)&#8230;(D.3)<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=13\">Proof of coloration theorems (D.4)&#8230;(D.7)<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=14\">Proof of (D.7) cont. and of (D.8)<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=15\">Figure illustrating the proof of (D.8)<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=16\">Proof of coloration theorem S<sub>2<\/sub><\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=17\">Proof of coloration theorem (E.1)&#8230;(E.9)<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=18\">Proof of (E.9) cont. &#8230; (E.13)<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=19\">Proof of (E.13) cont. &#8230; (E.15)<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=20\">Statement of the Construction theorems<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=21\">Proof of Construction Theorems I, II<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=22\">Proof of construction theorem II, cont.<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=23\">Proof of construction theorem II, cont<sup>2<\/sup>.<\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=24\">Proof of Theorem A<sub>1<\/sub><\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=25\">Proof of Theorems A<sub>2<\/sub> and A<sub>3<\/sub><\/a><\/li>\n<li><a href=\"http:\/\/www.library.illinois.edu\/mtx\/wp-content\/uploads\/sites\/18\/2018\/08\/Haken1971.pdf#page=26\">Proof of Theorem A<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Paper information Title: Notes on Shimamoto\u2019s Construction Author: Wolfgang Haken Source: Manuscript, October 20-24, 1971 4 Color Seminar Received from: Wolfgang Haken, June 2018 by Professor Bertram Lud\u00e4scher, 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 [&hellip;]<\/p>\n","protected":false},"author":296,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-2092","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/pages\/2092","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/users\/296"}],"replies":[{"embeddable":true,"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/comments?post=2092"}],"version-history":[{"count":8,"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/pages\/2092\/revisions"}],"predecessor-version":[{"id":2261,"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/pages\/2092\/revisions\/2261"}],"wp:attachment":[{"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/media?parent=2092"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}