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## k-partite subgraph

For each \(k\in \mathbb{N}\) and each simple graph \(G=(V,E)\), prove that \(G\) has a \(k\)-partite subgraph \(H=(V',E')\) (i.e., \(H\) has chromatic number at most \(k\)) such that \(|E'|\ge (1-1/k)\cdot |E|\).