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- Eulerian_path abstract "In graph theory, an Eulerian trail (or Eulerian path) is a trail in a graph which visits every edge exactly once. Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail which starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg problem in 1736. Mathematically the problem can be stated like this:Given the graph on the right, is it possible to construct a path (or a cycle, i.e. a path starting and ending on the same vertex) which visits each edge exactly once?Euler proved that a necessary condition for the existence of Eulerian circuits is that all vertices in the graph have an even degree, and stated without proof that connected graphs with all vertices of even degree have an Eulerian circuit. The first complete proof of this latter claim was published posthumously in 1873 by Carl Hierholzer.The term Eulerian graph has two common meanings in graph theory. One meaning is a graph with an Eulerian circuit, and the other is a graph with every vertex of even degree. These definitions coincide for connected graphs.For the existence of Eulerian trails it is necessary that zero or two vertices have an odd degree; this means the Königsberg graph is not Eulerian. If there are no vertices of odd degree, all Eulerian trails are circuits. If there are exactly two vertices of odd degree, all Eulerian trails start at one of them and end at the other. A graph that has an Eulerian trail but not an Eulerian circuit is called semi-Eulerian.".
- Eulerian_path thumbnail Konigsburg_graph.svg?width=300.
- Eulerian_path wikiPageExternalLink message.jspa?messageID=3648262&tstart=135.
- Eulerian_path wikiPageExternalLink E053.html.
- Eulerian_path wikiPageID "333219".
- Eulerian_path wikiPageRevisionID "603985127".
- Eulerian_path hasPhotoCollection Eulerian_path.
- Eulerian_path subject Category:Graph_theory_objects.
- Eulerian_path type GraphTheoryObjects.
- Eulerian_path type Object100002684.
- Eulerian_path type PhysicalEntity100001930.
- Eulerian_path comment "In graph theory, an Eulerian trail (or Eulerian path) is a trail in a graph which visits every edge exactly once. Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail which starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg problem in 1736. Mathematically the problem can be stated like this:Given the graph on the right, is it possible to construct a path (or a cycle, i.e.".
- Eulerian_path label "Caminho euleriano".
- Eulerian_path label "Cammino euleriano".
- Eulerian_path label "Ciclo euleriano".
- Eulerian_path label "Eulerian path".
- Eulerian_path label "Eulerkreisproblem".
- Eulerian_path label "Graphe eulérien".
- Eulerian_path label "Łańcuch Eulera".
- Eulerian_path label "Эйлеров цикл".
- Eulerian_path label "オイラー路".
- Eulerian_path label "一笔画问题".
- Eulerian_path sameAs Eulerovský_tah.
- Eulerian_path sameAs Eulerkreisproblem.
- Eulerian_path sameAs Ciclo_euleriano.
- Eulerian_path sameAs Eulertar_grafo.
- Eulerian_path sameAs Graphe_eulérien.
- Eulerian_path sameAs Cammino_euleriano.
- Eulerian_path sameAs オイラー路.
- Eulerian_path sameAs 오일러_경로.
- Eulerian_path sameAs Łańcuch_Eulera.
- Eulerian_path sameAs Caminho_euleriano.
- Eulerian_path sameAs m.01x4_6.
- Eulerian_path sameAs Q624580.
- Eulerian_path sameAs Q624580.
- Eulerian_path sameAs Eulerian_path.
- Eulerian_path wasDerivedFrom Eulerian_path?oldid=603985127.
- Eulerian_path depiction Konigsburg_graph.svg.
- Eulerian_path isPrimaryTopicOf Eulerian_path.
