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Let G be k-critical graph with respect to vertex-arboricity (k>=3). Prove that for each vertex v of G, the graph G-v is not (k-1)-critical with respect to vertex-arboricity.

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Proof. If not, then there exists a vertex v of G such that G-v is (k-1)-critical which means that for each ...

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This is a proof regarding vertex-arboricity.