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

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