Differences
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| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
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k-partite_graph [2014/02/11 00:45] nikolaj |
k-partite_graph [2014/02/11 00:53] nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#88DDEE: $k\in\mathrm N$ | | | @#88DDEE: $k\in\mathrm N$ | | ||
| - | | @#88DDEE: $V,E$ ... set | | + | | @#88DDEE: $V$ ... set | |
| | @#FFBB00: $\langle V,E\rangle \in \mathrm{it}(E,V) $ | | | @#FFBB00: $\langle V,E\rangle \in \mathrm{it}(E,V) $ | | ||
| Line 9: | Line 9: | ||
| | @#DDDDDD: $ i,j\in\{1,\dots,k\} $ | | | @#DDDDDD: $ i,j\in\{1,\dots,k\} $ | | ||
| - | | @#DDDDDD: $ X_1,\dots,X_k\subset V$, $\forall i,j.\ X_i\cap X_j=\emptyset $ | | + | | @#DDDDDD: $ X_1,\dots,X_k\subset V $ | |
| + | | @#DDDDDD: $ \bigcup_i X_i=V $ | | ||
| + | | @#DDDDDD: $ \forall i,j.\ X_i\cap X_j=\emptyset $ | | ||
| | @#DDDDDD: $ v,w\in V $ | | | @#DDDDDD: $ v,w\in V $ | | ||
| - | | @#55EE55: $\exists X_1,\dots,X_k.\ \forall u,v.\ \{u,v\}\in E(\psi)\implies \forall i.\ \neg(v\in X_i\land w\in X_i) $ | | + | | @#55EE55: $\exists X_1,\dots,X_k.\ \forall u,v.\ \{u,v\}\in E\implies \forall i.\ \neg(v\in X_i\land w\in X_i) $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
