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An Eulerian trail, [note 1] or Euler walk, in an undirected graph is a walk that uses each edge exactly once. If such a walk exists, the graph is called traversable or semi-eulerian. [3] An Eulerian cycle, [note 1] also called an Eulerian circuit or Euler tour, in an undirected graph is a cycle that uses each edge exactly once
Euler's argument shows that a necessary condition for the walk of the desired form is that the graph be connected and have exactly zero or two nodes of odd degree. This condition turns out also to be sufficient—a result stated by Euler and later proved by Carl Hierholzer. Such a walk is now called an Eulerian trail or Euler walk in his honor ...
A path such that no graph edges connect two nonconsecutive path vertices is called an induced path. A path that includes every vertex of the graph without repeats is known as a Hamiltonian path . Two paths are vertex-independent (alternatively, internally disjoint or internally vertex-disjoint ) if they do not have any internal vertex or edge ...
Eulerian An Eulerian path is a walk that uses every edge of a graph exactly once. An Eulerian circuit (also called an Eulerian cycle or an Euler tour) is a closed walk that uses every edge exactly once. An Eulerian graph is a graph that has an Eulerian circuit.
The Euler tour technique (ETT), named after Leonhard Euler, is a method in graph theory for representing trees. The tree is viewed as a directed graph that contains two directed edges for each edge in the tree. The tree can then be represented as a Eulerian circuit of the directed graph, known as the Euler tour representation (ETR) of the tree
A visual timeline of the New Year’s attack that left at least 15 dead in New Orleans. News. Reuters. US considers potential rules to restrict or bar Chinese drones. Sports. Sports.
Ron Adar/Shutterstock. Scott Hamilton Figure Skating in Harlem's 26th Annual "Celebrating Excellence & Sisterhood" Gala, New York, USA - 24 Apr 2023
This can be translated into graph-theoretic terms as asking for an Euler path or Euler tour of a connected graph representing the city and its bridges: a walk through the graph that traverses each edge once, either ending at a different vertex than it starts in the case of an Euler path or returning to its starting point in the case of an Euler ...