TY - JOUR

T1 - Giant components in biased graph processes

AU - Amir, Gideon

AU - Gurel-Gurevich, Ori

AU - Lubetzky, Eyal

AU - Singer, Amit

PY - 2010

Y1 - 2010

N2 - A random graph process, G1(n), is a sequence of graphs on n vertices which begins with the edgeless graph, and where at each step a single edge is added according to a uniform distribution on the missing edges. It is well known that in such a process a giant component (of linear size) typically emerges after (1+o(1))n=2 edges (a phenomenon known as "the double jump"), i.e., at time t = 1 when using a timescale of n/2 edges in each step.

AB - A random graph process, G1(n), is a sequence of graphs on n vertices which begins with the edgeless graph, and where at each step a single edge is added according to a uniform distribution on the missing edges. It is well known that in such a process a giant component (of linear size) typically emerges after (1+o(1))n=2 edges (a phenomenon known as "the double jump"), i.e., at time t = 1 when using a timescale of n/2 edges in each step.

KW - Giant component

KW - Random graphs

KW - Wormald's differential equation method

UR - http://www.scopus.com/inward/record.url?scp=84856420821&partnerID=8YFLogxK

U2 - 10.1512/iumj.2010.59.4008

DO - 10.1512/iumj.2010.59.4008

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AN - SCOPUS:84856420821

SN - 0022-2518

VL - 59

SP - 1853

EP - 1888

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 6

ER -