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FindPostmanTour—Wolfram Documentation

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FindPostmanTour[g]

finds a Chinese postman tour in the graph g of minimal length.

Details

A Chinese postman tour is a tour that traverses each edge at least once.
FindPostmanTour returns a list of edges consisting of Chinese postman tours.
FindPostmanTour returns the list {} if no Chinese postman tours exist.
FindPostmanTour[g] is equivalent to FindPostmanTour[g,1].
FindPostmanTour works with undirected graphs, directed graphs, weighted graphs, and multigraphs.

Examplesopen all close all Basic Examples (2)

Find a Chinese postman tour:

Highlight the tour:

Find several Chinese postman tours:

Scope (8)

FindPostmanTour works with undirected graphs:

Directed graphs:

Weighted graphs:

Multigraphs:

Find several Chinese postman tours:

Use rules to specify the graph:

FindPostmanTour returns an empty result for a graph with no Chinese postman tours:

FindPostmanTour works with large graphs:

Applications (3)

Find a shortest route that a newspaper carrier can use to distribute newspapers in a neighborhood:

The total distance:

Find the most efficient way for a letter carrier to deliver letters, knowing the time it takes to deliver mail on a street and the time it takes to walk a street without delivering mail (deadheading time):

A route that goes through all the streets and minimizes the total deadheading time:

Show the route:

The total delivery time:

Testing combinations of actions in a finite-state machine:

Generate a line graph:

A length-2 switch cover:

Properties & Relations (2)

An Eulerian graph has a Chinese postman tour:

It is the same as its Eulerian cycle:

A connected graph has a Chinese postman tour:

Neat Examples (1)

Find a Chinese postman tour:

Dynamically highlight cycles:

Wolfram Research (2012), FindPostmanTour, Wolfram Language function, https://reference.wolfram.com/language/ref/FindPostmanTour.html (updated 2015). Text Wolfram Research (2012), FindPostmanTour, Wolfram Language function, https://reference.wolfram.com/language/ref/FindPostmanTour.html (updated 2015).CMS Wolfram Language. 2012. "FindPostmanTour." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/FindPostmanTour.html.APA Wolfram Language. (2012). FindPostmanTour. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindPostmanTour.htmlBibTeX @misc{reference.wolfram_2025_findpostmantour, author="Wolfram Research", title="{FindPostmanTour}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindPostmanTour.html}", note=[Accessed: 17-August-2025]}BibLaTeX @online{reference.wolfram_2025_findpostmantour, organization={Wolfram Research}, title={FindPostmanTour}, year={2015}, url={https://reference.wolfram.com/language/ref/FindPostmanTour.html}, note=[Accessed: 17-August-2025]}

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