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k-partite_graph [2014/02/11 00:52] nikolaj |
k-partite_graph [2014/03/21 11:11] (current) |
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| ===== k-partite graph ===== | ===== k-partite graph ===== | ||
| ==== Set ==== | ==== Set ==== | ||
| - | | @#88DDEE: $k\in\mathrm N$ | | + | | @#55CCEE: context | @#55CCEE: $k\in\mathrm N$ | |
| - | | @#88DDEE: $V$ ... set | | + | | @#55CCEE: context | @#55CCEE: $V$ ... set | |
| - | | @#FFBB00: $\langle V,E\rangle \in \mathrm{it}(E,V) $ | | + | | @#FFBB00: definiendum | @#FFBB00: $\langle V,E\rangle \in \mathrm{it}(E,V) $ | |
| - | | @#AAFFAA: $ \langle V,E\rangle $ ... undirected graph | | + | | @#AAFFAA: inclusion | @#AAFFAA: $ \langle V,E\rangle $ ... undirected graph | |
| - | | @#DDDDDD: $ i,j\in\{1,\dots,k\} $ | | + | | @#DDDDDD: range | @#DDDDDD: $ i,j\in\{1,\dots,k\} $ | |
| - | | @#DDDDDD: $ X_1,\dots,X_k\subset V$,\ \bigcup_i X_i=V,\ $\forall i,j.\ X_i\cap X_j=\emptyset $ | | + | | @#DDDDDD: range | @#DDDDDD: $ \bigcup_i X_i=V $ | |
| - | | @#DDDDDD: $ v,w\in V $ | | + | | @#DDDDDD: range | @#DDDDDD: $ \forall i,j.\ X_i\cap X_j=\emptyset $ | |
| + | | @#DDDDDD: range | @#DDDDDD: $ v,w\in V $ | | ||
| - | | @#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) $ | | + | | @#55EE55: postulate | @#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 ==== | ||
