TY - JOUR
T1 - Regular induced subgraphs of a random Graph
AU - Krivelevich, Michael
AU - Sudakov, Benny
AU - Wormald, Nicholas
PY - 2011/5
Y1 - 2011/5
N2 - An old problem of Erdos, Fajtlowicz, and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on $n$ vertices. Motivated by this problem, we consider the order of such a subgraph in a typical graph on $n$ vertices, i.e., in a binomial random graph $G(n,1/2)$. We prove that with high probability a largest induced regular subgraph of $G(n,1/2)$ has about $n^{2/3}$ vertices.
AB - An old problem of Erdos, Fajtlowicz, and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on $n$ vertices. Motivated by this problem, we consider the order of such a subgraph in a typical graph on $n$ vertices, i.e., in a binomial random graph $G(n,1/2)$. We prove that with high probability a largest induced regular subgraph of $G(n,1/2)$ has about $n^{2/3}$ vertices.
KW - Extremal graph theory
KW - Random graph
KW - Random regular graphs
KW - Regular induced subgraph
UR - http://www.scopus.com/inward/record.url?scp=79953010113&partnerID=8YFLogxK
U2 - 10.1002/rsa.20324
DO - 10.1002/rsa.20324
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AN - SCOPUS:79953010113
SN - 1042-9832
VL - 38
SP - 235
EP - 250
JO - Random Structures and Algorithms
JF - Random Structures and Algorithms
IS - 3
ER -