Editing Hamiltonian path (section)

==Definitions==
A ''Hamiltonian path'' or ''traceable path'' is a [[path (graph theory)|path]] that visits each vertex of the graph exactly once. A graph that contains a Hamiltonian path is called a '''traceable graph'''. A graph is '''Hamiltonian-connected''' if for every pair of vertices there is a Hamiltonian path between the two vertices.

A ''Hamiltonian cycle'', ''Hamiltonian circuit'', ''vertex tour'' or ''graph cycle'' is a [[cycle (graph theory)|cycle]] that visits each vertex exactly once. A graph that contains a Hamiltonian cycle is called a '''Hamiltonian graph'''.

Similar notions may be defined for ''[[directed graph]]s'', where each edge (arc) of a path or cycle can only be traced in a single direction (i.e., the vertices are connected with arrows and the edges traced "tail-to-head").

A [[Hamiltonian decomposition]] is an edge decomposition of a graph into Hamiltonian circuits.

A ''Hamilton maze'' is a type of logic puzzle in which the goal is to find the unique Hamiltonian cycle in a given graph.<ref>{{cite book |last=de Ruiter |first=Johan |date=2017 |title=Hamilton Mazes – The Beginner's Guide}}</ref><ref>{{cite web| url=http://www2.stetson.edu/~efriedma/puzzle/ham/ |title=Hamiltonian Mazes |last=Friedman |first=Erich |date=2009 |website=Erich's Puzzle Palace |access-date=27 May 2017 |url-status=live |archive-url=https://web.archive.org/web/20160416235225/http://www2.stetson.edu/~efriedma/puzzle/ham/ |archive-date=16 April 2016 }}</ref>