finds a Hamiltonian path in the graph g with the smallest total length.
FindHamiltonianPath [g,s,t]
finds a Hamiltonian path with the smallest total length from s to t.
FindHamiltonianPath
finds a Hamiltonian path in the graph g with the smallest total length.
FindHamiltonianPath [g,s,t]
finds a Hamiltonian path with the smallest total length from s to t.
Details and Options
- FindHamiltonianPath is also known as the Hamiltonian path problem.
- A Hamiltonian path visits each vertex exactly once.
- FindHamiltonianPath returns the list {} if no Hamiltonian path exists.
Examples
open all close allBasic Examples (1)
Find a Hamiltonian path through vertices in a graph:
Highlight the path:
Find a Hamiltonian path between two individual vertices in a graph:
Highlight the path:
Scope (3)
FindHamiltonianPath works with undirected graphs:
Weighted graphs:
FindHamiltonianPath works with large graphs:
Options (1)
DistanceFunction (1)
This defines a sparse distance matrix among six points:
Find a Hamiltonian path:
Highlight the path:
Applications (2)
Find a sequence of moves by a knight chess piece that visits each square of an 8×8 chessboard exactly once:
A knight's move:
Find a Hamiltonian path of Europe from Greece to Germany:
Latitude and longitude of geographical centers:
Construct a weighted graph of Europe:
Show the tour:
Properties & Relations (2)
A graph with a Hamiltonian path may not have a Hamiltonian cycle:
A graph with a Hamiltonian cycle has a Hamiltonian path:
Related Guides
History
Text
Wolfram Research (2015), FindHamiltonianPath, Wolfram Language function, https://reference.wolfram.com/language/ref/FindHamiltonianPath.html.
CMS
Wolfram Language. 2015. "FindHamiltonianPath." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FindHamiltonianPath.html.
APA
Wolfram Language. (2015). FindHamiltonianPath. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindHamiltonianPath.html
BibTeX
@misc{reference.wolfram_2025_findhamiltonianpath, author="Wolfram Research", title="{FindHamiltonianPath}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindHamiltonianPath.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_findhamiltonianpath, organization={Wolfram Research}, title={FindHamiltonianPath}, year={2015}, url={https://reference.wolfram.com/language/ref/FindHamiltonianPath.html}, note=[Accessed: 04-January-2026]}