Search results
Results from the WOW.Com Content Network
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
The first long-distance hiking trail in Europe was the National Blue Trail of Hungary, established in 1938. The formation of the European Union made transnational hiking trails possible. Today, the network consists of 12 paths and covers more than 65,000 kilometres (40,000 mi), crisscrossing Europe.
An Eulerian circuit is a directed closed trail that visits each edge exactly once. In 1736, Euler showed that G has an Eulerian circuit if and only if G is connected and the indegree is equal to outdegree at every vertex. In this case G is called Eulerian. We denote the indegree of a vertex v by deg(v).
A directed circuit is a non-empty directed trail (e 1, e 2, ..., e n) with a vertex sequence (v 1, v 2, ..., v n, v 1). A directed cycle or simple directed circuit is a directed circuit in which only the first and last vertices are equal. [1] n is called the length of the directed circuit resp. length of the directed cycle.
Since the graph corresponding to historical Königsberg has four nodes of odd degree, it cannot have an Eulerian path. An alternative form of the problem asks for a path that traverses all bridges and also has the same starting and ending point. Such a walk is called an Eulerian circuit or an Euler tour. Such a circuit exists if, and only if ...
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
One of the worst ways to start the new year is with holiday debt and a looming tax bill. However, whether it's adjusting contributions or planning deductions, small, year-end actions can lead to...
Create duplicates for every edge to create an Eulerian graph. Find an Eulerian tour for this graph. Convert to TSP: if a city is visited twice, then create a shortcut from the city before this in the tour to the one after this. To improve the lower bound, a better way of creating an Eulerian graph is needed.