I need this proof:
Let $G$ be a graph such that $\chi (H) <\chi (G)$ for every subgraph $H$ of $G$. A graph is called $k$-critical, if in addition $\chi (G) = k$. Prove that $\chi (G) ≤ \delta + 1$.
Graph Coloring Proof χ (G) ≤ δ + 1 for k-criticals
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