Editing Path (graph theory) (section)

{{Short description|Sequence of edges which join a sequence of nodes on a given graph}}
{{For|the family of graphs known as paths|Path graph}}

[[File:Snake-in-the-box and Hamiltonian path.svg|thumb|right|A three-dimensional [[hypercube graph]] showing a [[Hamiltonian path]] in red, and a [[Snake-in-the-box|longest induced path]] in bold black]]

In [[graph theory]], a '''path''' in a [[Graph (discrete mathematics)|graph]] is a finite or infinite [[sequence]] of [[Edge (graph theory)|edges]] which joins a sequence of [[Vertex (graph theory)|vertices]] which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges). A '''directed path''' (sometimes called '''dipath'''{{sfn|McCuaig|1992|p=205}}) in a [[directed graph]] is a finite or infinite sequence of edges which joins a sequence of distinct vertices, but with the added restriction that the edges be all directed in the same direction.

Paths are fundamental concepts of graph theory, described in the introductory sections of most graph theory texts. See e.g. {{harvtxt|Bondy|Murty|1976}}, {{harvtxt|Gibbons|1985}}, or {{harvtxt|Diestel|2005}}. {{harvtxt|Korte|Lovász|Prömel|Schrijver|1990}} cover more advanced [[algorithm]]ic topics concerning paths in graphs.