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- Q7959587 subject Q7007191.
- Q7959587 subject Q7494515.
- Q7959587 subject Q8498914.
- Q7959587 abstract "In graph theory, Wagner's theorem is a mathematical forbidden graph characterization of planar graphs, named after Klaus Wagner, stating that a finite graph is planar if and only if its minors include neither K5 (the complete graph on five vertices) nor K3,3 (the utility graph, a complete bipartite graph on six vertices). This was one of the earliest results in the theory of graph minors and can be seen as a forerunner of the Robertson–Seymour theorem.".
- Q7959587 thumbnail Petersen_Wagner_minors.svg?width=300.
- Q7959587 wikiPageWikiLink Q1304193.
- Q7959587 wikiPageWikiLink Q131476.
- Q7959587 wikiPageWikiLink Q141488.
- Q7959587 wikiPageWikiLink Q1415372.
- Q7959587 wikiPageWikiLink Q17086290.
- Q7959587 wikiPageWikiLink Q222032.
- Q7959587 wikiPageWikiLink Q2642629.
- Q7959587 wikiPageWikiLink Q3115543.
- Q7959587 wikiPageWikiLink Q3115621.
- Q7959587 wikiPageWikiLink Q32918.
- Q7959587 wikiPageWikiLink Q3527155.
- Q7959587 wikiPageWikiLink Q45715.
- Q7959587 wikiPageWikiLink Q5134410.
- Q7959587 wikiPageWikiLink Q5467387.
- Q7959587 wikiPageWikiLink Q547823.
- Q7959587 wikiPageWikiLink Q5597085.
- Q7959587 wikiPageWikiLink Q5597098.
- Q7959587 wikiPageWikiLink Q5597156.
- Q7959587 wikiPageWikiLink Q584521.
- Q7959587 wikiPageWikiLink Q7007191.
- Q7959587 wikiPageWikiLink Q739462.
- Q7959587 wikiPageWikiLink Q7494515.
- Q7959587 wikiPageWikiLink Q837902.
- Q7959587 wikiPageWikiLink Q8498914.
- Q7959587 wikiPageWikiLink Q898572.
- Q7959587 wikiPageWikiLink Q905837.
- Q7959587 wikiPageWikiLink Q913598.
- Q7959587 wikiPageWikiLink Q96013.
- Q7959587 comment "In graph theory, Wagner's theorem is a mathematical forbidden graph characterization of planar graphs, named after Klaus Wagner, stating that a finite graph is planar if and only if its minors include neither K5 (the complete graph on five vertices) nor K3,3 (the utility graph, a complete bipartite graph on six vertices). This was one of the earliest results in the theory of graph minors and can be seen as a forerunner of the Robertson–Seymour theorem.".
- Q7959587 label "Wagner's theorem".
- Q7959587 depiction Petersen_Wagner_minors.svg.