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 -