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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 858.05057

**Autor: ** Erdös, Paul; Reid, Talmage James; Schelp, Richard; Staton, William

**Title: ** Sizes of graphs with induced subgraphs of large maximum degree. (In English)

**Source: ** Discrete Math. 158, No.1-3, 283-286 (1996).

**Review: ** The following conjecture is considered: Let n \geq k \geq j \geq 1 and n \geq 3, let G be a graph with n+k vertices in which every n+j vertices induce a subgraph which contains a vertex of degree at least n. Then G has at least (k-j+1)n+\binom{k-j+1}{2} edges.

The authors prove that this conjecture holds for j \geq 2 and n \geq **max****{**j(k-j),\binom{k-j+2}{2}**}**.

**Reviewer: ** B.Zelinka (Liberec)

**Classif.: ** * 05C35 Extremal problems (graph theory)

**Keywords: ** minimum degree; induced subgraph

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag