TY - JOUR

T1 - Induced subgraphs of prescribed size

AU - Alon, Noga

AU - Krivelevich, Michael

AU - Sudakov, Benny

PY - 2003/8

Y1 - 2003/8

N2 - A subgraph of a graph G is called trivial if it is either a clique or an independent set. Let q(G) denote the maximum number of vertices in a trivial subgraph of G. Motivated by an open problem of Erdos and McKay we show that every graph G on n vertices for which q(G) ≤ C log n contains an induced subgraph with exactly y edges, for every y between 0 and nδ(C). Our methods enable us also to show that under much weaker assumption, i.e., q(G) ≤ n/14, G still must contain an induced subgraph with exactly y edges, for every y between 0 and eΩ(√log n).

AB - A subgraph of a graph G is called trivial if it is either a clique or an independent set. Let q(G) denote the maximum number of vertices in a trivial subgraph of G. Motivated by an open problem of Erdos and McKay we show that every graph G on n vertices for which q(G) ≤ C log n contains an induced subgraph with exactly y edges, for every y between 0 and nδ(C). Our methods enable us also to show that under much weaker assumption, i.e., q(G) ≤ n/14, G still must contain an induced subgraph with exactly y edges, for every y between 0 and eΩ(√log n).

KW - Cliques and independent sets

KW - Induced subgraphs

KW - Ramsey graphs

UR - http://www.scopus.com/inward/record.url?scp=0043240128&partnerID=8YFLogxK

U2 - 10.1002/jgt.10117

DO - 10.1002/jgt.10117

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AN - SCOPUS:0043240128

VL - 43

SP - 239

EP - 251

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 4

ER -