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bipartite_graph [2014/02/11 00:54] nikolaj |
bipartite_graph [2014/04/06 14:51] nikolaj |
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| ===== Bipartite graph ===== | ===== Bipartite graph ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $V$ ... set | | + | | @#55CCEE: context | @#55CCEE: $V$ ... set | |
| - | + | | @#FFBB00: definiendum | @#FFBB00: $\langle V,E\rangle \in \mathrm{it}(E,V) $ | | |
| - | | @#FFBB00: $\langle V,E\rangle \in \mathrm{it}(E,V) $ | | + | | @#55EE55: postulate | @#55EE55: $ \langle V,E\rangle $ ... undirected graph | |
| - | + | | @#DDDDDD: range | @#DDDDDD: $ X\cup Y=V $ | | |
| - | | @#55EE55: $ \langle V,E\rangle $ ... undirected graph | | + | | @#DDDDDD: range | @#DDDDDD: $ X\cap Y=\emptyset $ | |
| - | + | | @#DDDDDD: range | @#DDDDDD: $ v,w\in V $ | | |
| - | | @#DDDDDD: $ X\cup Y=V $ | | + | | @#55EE55: postulate | @#55EE55: $\exists X,Y.\ \forall u,v.\ \{u,v\}\in E\implies \neg(u\in X\land v\in X)\land \neg(v\in Y\land u\in Y) $ | |
| - | | @#DDDDDD: $ X\cap Y=\emptyset $ | | + | |
| - | | @#DDDDDD: $ v,w\in V $ | | + | |
| - | + | ||
| - | | @#55EE55: $\exists X,Y.\ \forall u,v.\ \{u,v\}\in E\implies \neg(u\in X\land v\in X)\land \neg(v\in Y\land u\in Y) $ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
