Critical random graphs: Diameter and mixing time
نویسندگان
چکیده
منابع مشابه
Critical Random Graphs: Diameter and Mixing Time1 by Asaf Nachmias
Let C1 denote the largest connected component of the critical Erdős– Rényi random graph G(n, 1 n ). We show that, typically, the diameter of C1 is of order n1/3 and the mixing time of the lazy simple random walk on C1 is of order n. The latter answers a question of Benjamini, Kozma and Wormald. These results extend to clusters of size n2/3 of p-bond percolation on any d-regular n-vertex graph w...
متن کاملMixing time of near-critical random graphs
Let C1 be the largest component of the Erdős–Rényi random graph G(n,p). The mixing time of random walk on C1 in the strictly supercritical regime, p = c/n with fixed c > 1, was shown to have order log n by Fountoulakis and Reed, and independently by Benjamini, Kozma and Wormald. In the critical window, p = (1 + ε)/n where λ= εn is bounded, Nachmias and Peres proved that the mixing time on C1 is...
متن کاملCritical Random Graphs: Diameter and Mixing Time Asaf Nachmias and Yuval Peres
Let C1 denote the largest connected component of the critical ErdősRényi random graph G(n, 1 n ). We show that, typically, the diameter of C1 is of order n and the mixing time of the lazy simple random walk on C1 is of order n. The latter answers a question of Benjamini, Kozma and Wormald [5]. These results extend to clusters of size n of p-bond percolation on any d-regular n-vertex graph where...
متن کاملDiameter critical graphs
A graph is called diameter-k-critical if its diameter is k, and the removal of any edge strictly increases the diameter. In this paper, we prove several results related to a conjecture often attributed to Murty and Simon, regarding the maximum number of edges that any diameter-k-critical graph can have. In particular, we disprove a longstanding conjecture of Caccetta and Häggkvist (that in ever...
متن کاملThe Diameter of Random Graphs
Extending some recent theorems of Klee and Larman, we prove rather sharp results about the diameter of a random graph. Among others we show that if d = d(n) > 3 and m = m(n) satisfy (log n)/d 3 log log n -> oo, 2rf_Imd'/'nd+x log n -» oo and dd~2md~l/nd — log n -» -oo then almost every graph with n labelled vertices and m edges has diameter d. About twenty years ago Erdös [7], [8] used random g...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2008
ISSN: 0091-1798
DOI: 10.1214/07-aop358