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Eulerian path

In graph theory, an Eulerian trail (or Eulerian path) is a trail in a finite graph that visits every edge exactly once (allowing for revisiting vertices). Similarly, an Eulerian circuit or Eulerian cycle is an Eulerian trail that starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of…

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Overview

Definition

Properties

Constructing Eulerian trails and circuits

Counting Eulerian circuits

Applications

In infinite graphs

Mixed Eulerian graphs

Eulerian cycles and bridges

Bibliography

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Eulerian path

Nodes85
Edges84
Triples8
Avg. degree1.98
Density0.023529
Components1

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Eulerian path

Top relations

see also · 4
Eulerian path → Euler, Eulerian, Route, Veblen's

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Important terminology

eulerian graph degree connected vertices vertex graphs even every trail undirected cycle edges algorithm euler edge two odd directed circuits

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
a doubly linked list to maintain the set of unused edges incident to each vertexinstance ofrepeating the previous step will exhaust all edges of the graph.By using a data structure0.80text
to maintain the list of vertices on the current tour that have unused edgesinstance ofrepeating the previous step will exhaust all edges of the graph.By using a data structure0.80text
and to maintain the tour itselfinstance ofrepeating the previous step will exhaust all edges of the graph.By using a data structure0.80text
the individual operations of the algorithminstance ofrepeating the previous step will exhaust all edges of the graph.By using a data structure0.80text
Eulerian pathsee alsoEulerian0.60section
Eulerian pathsee alsoEuler0.60section
Eulerian pathsee alsoRoute0.60section
Eulerian pathsee alsoVeblen's0.60section

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