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- Veblens_theorem abstract "In mathematics, Veblen's theorem, introduced by Oswald Veblen (1912), states that the set of edges of a finite graph can be written as a union of disjoint simple cycles if and only if every vertex has even degree. Thus, it is closely related to the theorem of Euler (1736) that a finite graph has an Euler tour (a single non-simple cycle that covers the edges of the graph) if and only if it is connected and every vertex has even degree. Indeed, a representation of a graph as a union of simple cycles may be obtained from an Euler tour by repeatedly splitting the tour into smaller cycles whenever there is a repeated vertex. However, Veblen's theorem applies also to disconnected graphs, and can be generalized to infinite graphs in which every vertex has finite degree (Sabidussi 1964).If a countably infinite graph G has no odd-degree vertices, then it may be written as a union of disjoint (finite) simple cycles if and only if every finite subgraph of G can be extended (by adding more edges and vertices of G) to a finite Eulerian graph. In particular, every countably infinite graph with only one end and with no odd vertices can be written as a union of disjoint cycles (Sabidussi 1964).".
- Veblens_theorem wikiPageExternalLink E053.pdf.
- Veblens_theorem wikiPageID "33868930".
- Veblens_theorem wikiPageLength "2597".
- Veblens_theorem wikiPageOutDegree "11".
- Veblens_theorem wikiPageRevisionID "675110539".
- Veblens_theorem wikiPageWikiLink Annals_of_Mathematics.
- Veblens_theorem wikiPageWikiLink Canadian_Journal_of_Mathematics.
- Veblens_theorem wikiPageWikiLink Category:Theorems_in_graph_theory.
- Veblens_theorem wikiPageWikiLink Connected_graph.
- Veblens_theorem wikiPageWikiLink Connectivity_(graph_theory).
- Veblens_theorem wikiPageWikiLink Cycle_(graph_theory).
- Veblens_theorem wikiPageWikiLink Cycle_basis.
- Veblens_theorem wikiPageWikiLink Cycle_double_cover.
- Veblens_theorem wikiPageWikiLink Cycle_double_cover_conjecture.
- Veblens_theorem wikiPageWikiLink End_(graph_theory).
- Veblens_theorem wikiPageWikiLink Euler_tour.
- Veblens_theorem wikiPageWikiLink Eulerian_matroid.
- Veblens_theorem wikiPageWikiLink Eulerian_path.
- Veblens_theorem wikiPageWikiLink Glossary_of_graph_theory.
- Veblens_theorem wikiPageWikiLink Infinite_graph.
- Veblens_theorem wikiPageWikiLinkText "Veblen's theorem".
- Veblens_theorem authorlink "Oswald Veblen".
- Veblens_theorem first "Oswald".
- Veblens_theorem hasPhotoCollection Veblens_theorem.
- Veblens_theorem last "Veblen".
- Veblens_theorem wikiPageUsesTemplate Template:Citation.
- Veblens_theorem wikiPageUsesTemplate Template:Harv.
- Veblens_theorem wikiPageUsesTemplate Template:Harvs.
- Veblens_theorem wikiPageUsesTemplate Template:Harvtxt.
- Veblens_theorem year "1912".
- Veblens_theorem subject Category:Theorems_in_graph_theory.
- Veblens_theorem comment "In mathematics, Veblen's theorem, introduced by Oswald Veblen (1912), states that the set of edges of a finite graph can be written as a union of disjoint simple cycles if and only if every vertex has even degree. Thus, it is closely related to the theorem of Euler (1736) that a finite graph has an Euler tour (a single non-simple cycle that covers the edges of the graph) if and only if it is connected and every vertex has even degree.".
- Veblens_theorem label "Veblen's theorem".
- Veblens_theorem sameAs m.0hndvpj.
- Veblens_theorem sameAs Теорема_Веблена.
- Veblens_theorem sameAs Q7917710.
- Veblens_theorem sameAs Q7917710.
- Veblens_theorem wasDerivedFrom Veblens_theoremoldid=675110539.
- Veblens_theorem isPrimaryTopicOf Veblens_theorem.