# HamiltonianGraphQ

yields True if the graph g is Hamiltonian, and False otherwise.

# Details • A graph is Hamiltonian if it has a cycle that traverses each vertex exactly once.

# Examples

open allclose all

## Basic Examples(2)

Test whether a graph is Hamiltonian:

Not all graphs have a Hamiltonian cycle:

## Scope(6)

HamiltonianGraphQ works with undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

HamiltonianGraphQ gives False for expressions that are not graphs:

HamiltonianGraphQ works with large graphs:

## Applications(2)

Test whether the Icosian game [MathWorld] has a solution:

A Hamiltonian cycle:

Test whether there is a sequence of moves by a knight chess piece that visits each square of an chessboard exactly once:

## Properties & Relations(4)

A Hamiltonian cycle can be found using FindHamiltonianCycle:

Skeleton graphs of platonic solids are Hamiltonian:

The line graph of a Hamiltonian graph is Hamiltonian:

An Eulerian graph is not always Hamiltonian:

The line graph of an Eulerian graph is Hamiltonian:

Introduced in 2010
(8.0)