## Path . graph theory

### 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.

### Parents

#### Subset of

#### Context