===== Path . graph theory =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $V,E$ ... set |

| @#FFBB00: definiendum | @#FFBB00: $\langle V,E,\psi\rangle \in \mathrm{it}(E,V) $ |

| @#55EE55: postulate   | @#55EE55: $\langle V,E,\psi\rangle $ ... simple graph |

| @#DDDDDD: range       | @#DDDDDD: $ u,v\in V $ |
| @#DDDDDD: range       | @#DDDDDD: $ a$ ... sequence in $V$  |
| @#DDDDDD: range       | @#DDDDDD: $ i\in\mathbb N$ |

| @#55EE55: postulate   | @#55EE55: $d(v)\neq 0$ | 
| @#55EE55: postulate   | @#55EE55: $ \exists a.\ \forall u,v.\ (\exists i.\ \{a_{i},a_{i+1}\}=\{u,v\}) \leftrightarrow (\{u,v\}\dots\mathrm{edge}) $ |

==== Discussion ====
A path is a graph which can fully be described by a sequence of vertices.
=== Theorems ===
The only paths which are non-bipartite are cycles of odd order.
==== Parents ====
=== Subset of ===
[[Simple graph]], [[Connected graph]]
=== Context ===
[[Sequence]], [[Vertex degree]]