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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. If such a cycle exists, the graph is called Eulerian or unicursal. [4] The term "Eulerian graph" is also sometimes used in a weaker sense to denote a graph where every vertex has even degree.
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 path or Euler walk in his honor ...
English: Using Eulerian paths to draw shapes with a continuous stroke by CMG Lee. 1. As the Haus vom Nikolaus puzzle has two odd vertices (orange), the path must start at one and end at the other. 2. The Annie Pope one with four odd vertices has no solution. 3. If there are no odd vertices, the path can start anywhere and forms a closed circuit. 4.
The puzzle consists of five rooms, which can be thought of as being connected by doorways. The five-room puzzle is a classical, [1] popular puzzle involving a large rectangle divided into five "rooms". The objective of the puzzle is to cross each "wall" of the diagram with a continuous line only once. [2]
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The College Football Playoff bracket is finally set and Caroline Fenton, Jason Fitz & Adam Breneman react to the final rankings and share what things the committee got right and which were wrong.
The Bristol Bridges Walk is a circular hiking route that is linked to the Königsberg bridge problem, a mathematical puzzle, which laid the foundation for graph theory, the mathematical study of networks. [2] [3] [4] The Bristol Bridges Walk presents a solution of the puzzle for the city of Bristol. [5]