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Fix version with counting argument for the first example |
→First example: Use the same form as in probabilistic version |
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* Of these colorings, only 2 colorings are 'bad' for that subgraph (the colorings in which all vertices are red or all vertices are blue).
* Hence, the total number of colorings that are bad for some (at least one) subgraph is at most <math>2 {n \choose r} 2^{{n \choose 2} - {r \choose 2}}</math>.
* Hence, if <math>2 {n \choose r} 2^{{n \choose 2} - {r \choose 2}} < 2^{n \choose 2} \Leftrightarrow
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