Abstract
A graphH isd-degenerate if every subgraph of it contains a vertex of degree smaller thand. For a graphG, letα d (G) denote the maximum number of vertices of an inducedd-degenerate subgraph ofG. Sharp lowers bounds forα d (G) in terms of the degree sequence ofG are obtained, and the minimum number of edges of a graphG withn vertices andα 2 (G) ≤ m is determined precisely for allm ≤ n.
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