Cycles: Difference between revisions
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===Graphs=== | ===Graphs=== | ||
On a graph, an Euler | On a graph, an '''Euler Path''' is a path through the graph that traverses every edge of the graph exactly once. | ||
An ''Euler Cycle'' is slightly more restrictive - it is a path through the graph that visits every edge of the graph exactly once, '''and''' it starts and ends on the same node of the graph. | |||
==Related== | ==Related== | ||
Revision as of 22:09, 26 April 2019
What is a cycle
There are actually two definitions of cycles - one applies to problems involving permutations and combinatorics, while the other applies to graphs.
Combinatorics
In combinatorics, a cycle is a way to write a given permutation in a unique way using one-line notation.
(Permutations can also be written using two-line notation, where the first row consists of all items in their natural order, and the second row consists of the items in the order specified by the permutation, but the two-row representation is not unique.)
Graphs
On a graph, an Euler Path is a path through the graph that traverses every edge of the graph exactly once.
An Euler Cycle is slightly more restrictive - it is a path through the graph that visits every edge of the graph exactly once, and it starts and ends on the same node of the graph.
Related
Graphs:
Permutations:
Flags
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Combinatorics
Combinatorial Structures - Order Does Not Matter Ordinary generating functions
Labelled Structures - Order Matters Enumerating Permutations: String Permutations Generating Permutations: Cool · Algorithm M (add-one) · Algorithm G (Gray binary code)
Combinatorics Problems Longest Increasing Subsequence · Maximum Value Contiguous Subsequence · Racing Gems Cards (poker hands with a deck of 52 playing cards)
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The Art of Computer Programming notes from reading Donald Knuth's Art of Computer Programming
Part of the 2017 CS Study Plan.
Mathematical Foundations: AOCP/Infinite Series · AOCP/Binomial Coefficients · AOCP/Multinomial Coefficients AOCP/Harmonic Numbers · AOCP/Fibonacci Numbers Puzzles/Exercises:
Volume 2: Seminumerical Algorithms
Volume 3: Sorting and Searching AOCP/Combinatorics · AOCP/Multisets · Rubiks Cube/Permutations
AOCP/Combinatorial Algorithms · AOCP/Boolean Functions AOCP/Five Letter Words · Rubiks Cube/Tuples AOCP/Generating Permutations and Tuples
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