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Euler and Hamiltonian Paths and Circuits Lumen Learning ...
https://courses.lumenlearning.com/math4liberalarts/chapter/introduction-euler-paths/
Use Fleury’s algorithm to find an Euler circuit; Add edges to a graph to create an Euler circuit if one doesn’t exist; Identify whether a graph has a Hamiltonian circuit or path; Find the optimal Hamiltonian circuit for a graph using the brute force algorithm, the nearest neighbor algorithm, and the sorted edges algorithm
Hamiltonian Circuits Mathematics for the Liberal Arts
https://courses.lumenlearning.com/waymakermath4libarts/chapter/hamiltonian-circuits/
Use Fleury’s algorithm to find an Euler circuit; Add edges to a graph to create an Euler circuit if one doesn’t exist; Identify whether a graph has a Hamiltonian circuit or path; Find the optimal Hamiltonian circuit for a graph using the brute force algorithm, the nearest neighbor algorithm, and the sorted edges algorithm
Hamiltonian path - Wikipedia
https://en.wikipedia.org/wiki/Hamiltonian_path
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a Hamiltonian path that is a cycle.Determining whether such paths and cycles exist in graphs is the Hamiltonian path problem, which is NP-complete.
Euler and Hamiltonian Paths
https://www2.cs.sfu.ca/~ggbaker/zju/math/euler-ham.html
Euler Paths and Circuits. An Euler circuit (or Eulerian circuit) in a graph \(G\) is a simple circuit that contains every edge of \(G\).. Reminder: a simple circuit doesn't use the same edge more than once. So, a circuit around the graph passing by every edge exactly once.
Algorithm for knight’s tour in Python – sophie's blog
http://blog.justsophie.com/algorithm-for-knights-tour-in-python/
In Discrete class, we’ve been talking about planar graphs and stuff like Hamilton traversals. One of our in-class exercises involved the knight’s tour, and whether we could find a rule that would allow us to decided if a knight’s tour was possible given a chessboard of a certain dimension.
Chapter 6: The Mathematics of Touring
https://www.math.upenn.edu/~rimmer/math170/notes/unit6part4.pdf
Step 1. Make a list of allthe possible Hamilton circuits of the graph. Each of these circuits represents a tour of the vertices of the graph. Step 2. For each tour calculate its weight (i.e., add the weights of all the edges in the circuit). Step 3. Choose an optimaltour (there is always more than one optimal tour to choose from!). ALGORITHM 1 ...
Knight's tour - Wikipedia
https://en.wikipedia.org/wiki/Knight%27s_tour
The earliest known reference to the knight's tour problem dates back to the 9th century AD. In Rudraṭa's Kavyalankara (5.15), a Sanskrit work on Poetics, the pattern of a knight's tour on a half-board has been presented as an elaborate poetic figure (citra-alaṅkāra) called the turagapadabandha or 'arrangement in the steps of a horse'. The same verse in four lines of eight syllables each ...
Eulerian path - Wikipedia
https://en.wikipedia.org/wiki/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 Königsberg problem in 1736.
Math for Liberal Studies: Using the Nearest-Neighbor Algorithm
https://www.youtube.com/watch?v=G8a8bJuQxnw
Jun 29, 2011 · In this video, we use the nearest-neighbor algorithm to find a Hamiltonian circuit for a given graph. For more info, visit the Math for Liberal Studies homep...Author: James Hamblin
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