{"id":2062,"date":"2018-08-17T15:20:45","date_gmt":"2018-08-17T15:20:45","guid":{"rendered":"http:\/\/wordpress.library.illinois.edu\/mtx\/?page_id=2062"},"modified":"2018-08-24T18:49:05","modified_gmt":"2018-08-24T18:49:05","slug":"uberprufung-des-beweises-fur-den-vierfarbensatz","status":"publish","type":"page","link":"https:\/\/wordpress.library.illinois.edu\/mtx\/uberprufung-des-beweises-fur-den-vierfarbensatz\/","title":{"rendered":"U. Schmidt (1982), \u00dcberpr\u00fcfung des beweises f\u00fcr den Vierfarbensatz"},"content":{"rendered":"

<\/p>\n

Paper information<\/h3>\n

<\/strong><\/p>\n\n\n
\nTitle:<\/strong> \u00dcberpr\u00fcfung des beweises f\u00fcr den Vierfarbensatz
\nAuthor:<\/strong> Ulrich Schmidt
\nSource:<\/strong> Diplomarbeit, Matr.-Nr. 066040, Mai 1982
\nLehrgebiet Allgemeine Elektrotechnik und Datenverarbeitung,
\nRheinisch-Westf\u00e4lische Technische Hochschule Aachen
\nReceived from:<\/strong> Ulrich Schmidt, June 2018 by Professor Bertram Lud\u00e4scher<\/a>, School of Information Sciences
\nAccess provided by the Mathematics Library<\/a> of the University of Illinois at Urbana-Champaign with the permission of Ulrich Schmidt.
\nAvailable online:<\/strong> since August 2018\n<\/td>\n		\n\"Schmidt1982_frontpage\"<\/a>\n<\/td>\n<\/tr>\n<\/table>\n

<\/p>\n

Table of Contents<\/strong><\/h3>\n<\/p>\n

    \n
  1. EINF\u00dcHRUNG<\/a><\/li>\n
  2. BEGRIFFE UND DEFINITIONEN DER GRAPHENTHEORIE<\/a><\/li>\n

    2.1. Definitionen<\/a>
    \n     2.2. Kantenfolgen und Zusammenhang<\/a>
    \n     2.3. Ebene Graphen<\/a><\/p>\n

  3. DIE GESCHICHTE DES VIERFARBENSATZES<\/a><\/li>\n

    3.1. Kempes Beweis<\/a>
    \n     3.2. Der F\u00fcnffarbensatz<\/a><\/p>\n

  4. REDUZIERBARKEIT<\/a><\/li>\n

    4.1. Definitionen<\/a>
    \n     4.2. Reduktionsarten<\/a><\/p>\n

  5. ENTLADUNGSPROZEDUREN<\/a><\/li>\n

    5.1. Der Graph als elektrisches Netzwerk<\/a>
    \n     5.2. Eine einfache Entladungsprozedur<\/a>
    \n     5.3. Reduktionshindernisse<\/a>
    \n     5.4. Die Entladungsprozedur von Appel und Haken<\/a><\/p>\n

  6. \u00dcBERPR\u00dcFUNG DES BEWEISES<\/a><\/li>\n

    6.1. Vorgehensweise<\/a>
    \n     6.2. Datenstrukturen<\/a>
    \n     6.3. Randkreise<\/a>
    \n     6.4. Der Verschmelzungsalgorithmus<\/a>
    \n     6.5. Auffinden reduzibler Teilfiguren<\/a>
    \n     6.6. Die Prozedur ‘entlade’<\/a>
    \n     6.7. Ergebnisse<\/a><\/p>\n

  7. PHILOSOPHISCHE AUSWIRKUNGEN DES VIERFARBENPROBLEMS<\/a><\/li>\n
  8. ANHANG<\/a><\/li>\n

    A. Das Programm ‘Entladung’<\/a>
    \n     B. Output<\/a>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

    Paper information Title: \u00dcberpr\u00fcfung des beweises f\u00fcr den Vierfarbensatz Author: Ulrich Schmidt Source: Diplomarbeit, Matr.-Nr. 066040, Mai 1982 Lehrgebiet Allgemeine Elektrotechnik und Datenverarbeitung, Rheinisch-Westf\u00e4lische Technische Hochschule Aachen Received from: Ulrich Schmidt, 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 […]<\/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-2062","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/pages\/2062","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=2062"}],"version-history":[{"count":20,"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/pages\/2062\/revisions"}],"predecessor-version":[{"id":2259,"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/pages\/2062\/revisions\/2259"}],"wp:attachment":[{"href":"https:\/\/wordpress.library.illinois.edu\/mtx\/wp-json\/wp\/v2\/media?parent=2062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}