The Euler Cycle Or Tour Problem

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Eulerian Cycle -- from Wolfram MathWorld

https://mathworld.wolfram.com/EulerianCycle.html

Aug 24, 2020 · An Eulerian cycle, also called an Eulerian circuit, Euler circuit, Eulerian tour, or Euler tour, is a trail which starts and ends at the same graph vertex. In other words, it is a graph cycle which uses each graph edge exactly once. For technical reasons, Eulerian cycles are mathematically easier to study than are Hamiltonian cycles. An Eulerian cycle for the octahedral graph is illustrated above.

Eulerian path and circuit for undirected graph - GeeksforGeeks

https://www.geeksforgeeks.org/eulerian-path-and-circuit/

Jun 13, 2013 · A graph is called Eulerian if it has an Eulerian Cycle and called Semi-Eulerian if it has an Eulerian Path. The problem seems similar to Hamiltonian Path which is NP complete problem for a general graph. Fortunately, we can find whether a given graph has a Eulerian …3.3/5

Eulerian Cycle Problem - FASTA

https://fasta.bioch.virginia.edu/cshl/pdf/16/taylor_3.pdf

•Find a tour through Königsberg that crosses every bridge exactly once •Euler: route inside land doesn’t matter, just the sequence of crossings •Abstraction: Graph •Land masses are vertices (nodes) •Bridges are Edges An Introduction to Bioinformatics Algorithms www.bioalgorithms.info Eulerian Cycle Problem • Find a cycle that

recursion - Python code to find Eulerian Tour does not ...

https://stackoverflow.com/questions/13435413/python-code-to-find-eulerian-tour-does-not-work-in-one-case-why

I am trying to solve a problem on Udacity described as follows: # Find Eulerian Tour # # Write a function that takes in a graph # represented as a list of tuples # and return a list of nodes that # you would follow on an Eulerian Tour # # For example, if the input graph was # [(1, 2), (2, 3), (3, 1)] # A possible Eulerian tour would be [1, 2, 3, 1]

What is a Euler or Eulerian tour?

https://iq.opengenus.org/what-is-a-euler-or-eulerian-tour/

An Euler tour or Eulerian tour in an undirected graph is a tour/ path that traverses each edge of the graph exactly once. Graphs that have an Euler tour are called Eulerian graphs. Necessary and sufficient conditions. An undirected graph has a closed Euler tour if and only if it …

Euler Paths and Circuits - Discrete Mathematics

http://discrete.openmathbooks.org/dmoi2/sec_paths.html

Section 4.4 Euler Paths and Circuits ¶ Investigate! 35. An Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. Our goal is to find a quick way to check whether a graph (or multigraph) has an Euler path or circuit.

Knight's tour - Wikipedia

https://en.wikipedia.org/wiki/Knight%27s_tour

The knight's tour problem is an instance of the more general Hamiltonian path problem in graph theory.The problem of finding a closed knight's tour is similarly an instance of the Hamiltonian cycle problem.Unlike the general Hamiltonian path problem, the knight's tour problem can be …

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