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bipartite_complete_graph [2014/02/08 00:40] nikolaj old revision restored (2014/02/08 00:30) |
bipartite_complete_graph [2014/02/08 00:55] nikolaj |
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| | @#DDDDDD: $ X\cap Y=\emptyset $ | | | @#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\in X),(y\in Y).\ \{x,y\}\in\mathrm{im}\ \psi) $ | | + | | @#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 ==== | ==== Discussion ==== | ||
| - | A bipartite complete graph is a bipartite graph where, if $X,Y$ are the two parts, for all $x\in X$ and for all $y\in Y$, there is an edge connecting those vertices. | + | 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 ==== | ==== Parents ==== | ||
| === Subset of === | === Subset of === | ||
| [[Bipartite graph]] | [[Bipartite graph]] | ||
