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bipartite_complete_graph [2014/02/08 00:55] nikolaj |
bipartite_complete_graph [2014/03/21 11:11] |
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| - | ===== Bipartite complete graph ===== | ||
| - | ==== Set ==== | ||
| - | | @#88DDEE: $V,E$ ... set | | ||
| - | | @#FFBB00: $\langle V,E,\psi\rangle \in \mathrm{it}(E,V) $ | | ||
| - | |||
| - | | @#55EE55: $\langle V,E,\psi\rangle $ ... undirected graph | | ||
| - | |||
| - | | @#DDDDDD: $ X\cap Y=\emptyset $ | | ||
| - | | @#DDDDDD: $ x\in X $ | | ||
| - | | @#DDDDDD: $ y\in Y $ | | ||
| - | |||
| - | | @#55EE55: $\exists X,Y.\ (\forall u,v.\ \{u,v\}\in\mathrm{im}(\psi)\implies (u\in X\land v\in Y)\lor (v\in X\land u\in Y)) \land (\forall x,y.\ \{x,y\}\in\mathrm{im}\ \psi $ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | Let $G$ be a bipartite complete graph with parts $X$ and $Y$. Then $G$ is bipartite complete if each $x\in X$ connects to each $y\in Y$. | ||
| - | ==== Parents ==== | ||
| - | === Subset of === | ||
| - | [[Bipartite graph]] | ||
