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path_._graph_theory [2014/02/09 03:17] nikolaj |
path_._graph_theory [2014/02/09 03:26] nikolaj |
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| | @#DDDDDD: $ i\in\mathbb N$ | | | @#DDDDDD: $ i\in\mathbb N$ | | ||
| - | | @#55EE55: $d(v)\ge 1$ | | + | | @#55EE55: $d(v)\neq 0$ | |
| | @#55EE55: $ \exists a.\ \forall u,v.\ (\exists i.\ \{a_{i},a_{i+1}\}=\{u,v\}) \leftrightarrow (\{u,v\}\dots\mathrm{edge}) $ | | | @#55EE55: $ \exists a.\ \forall u,v.\ (\exists i.\ \{a_{i},a_{i+1}\}=\{u,v\}) \leftrightarrow (\{u,v\}\dots\mathrm{edge}) $ | | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
| A path is a graph which can fully be described by a sequence of vertices. | 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 ==== | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
| [[Simple graph]], [[Connected graph]] | [[Simple graph]], [[Connected graph]] | ||
| === Requirements === | === Requirements === | ||
| - | [[Sequence]] | + | [[Sequence]], [[Vertex degree]] |
