## Path . graph theory

### Set

 context $V,E$ … set
 definiendum $\langle V,E,\psi\rangle \in \mathrm{it}(E,V)$
 postulate $\langle V,E,\psi\rangle$ … simple graph
 range $u,v\in V$ range $a$ … sequence in $V$ range $i\in\mathbb N$
 postulate $d(v)\neq 0$ postulate $\exists a.\ \forall u,v.\ (\exists i.\ \{a_{i},a_{i+1}\}=\{u,v\}) \leftrightarrow (\{u,v\}\dots\mathrm{edge})$

### 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.