hamiltonian_path#
- hamiltonian_path(G)[source]#
Returns a Hamiltonian path in the given tournament graph.
Each tournament has a Hamiltonian path. If furthermore, the tournament is strongly connected, then the returned Hamiltonian path is a Hamiltonian cycle (by joining the endpoints of the path).
- Parameters:
- GNetworkX graph
A directed graph representing a tournament.
- Returns:
- pathlist
A list of nodes which form a Hamiltonian path in
G
.
Notes
This is a recursive implementation with an asymptotic running time of \(O(n^2)\), ignoring multiplicative polylogarithmic factors, where \(n\) is the number of nodes in the graph.
Examples
>>> from networkx.algorithms import tournament >>> G = nx.DiGraph([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]) >>> tournament.hamiltonian_path(G) [0, 1, 2, 3]