Cover Time of a Random Graph With a Degree Sequence II: Allowing Vertices of Degree Two

被引：4

作者：

Cooper, Colin ^{[1
]}

Frieze, Alan ^{[2
]}

Lubetzky, Eyal ^{[3
]}

机构：

[1] Univ London, Kings Coll, Dept Comp Sci, London WC2R 2LS, England

[2] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA

[3] Microsoft Res, Redmond, WA 98052 USA

来源：

RANDOM STRUCTURES & ALGORITHMS | 2014年 / 45卷 / 04期

关键词：

random graphs; emerging giant; cover time; RANDOM-WALKS; GIANT COMPONENT;

D O I：

10.1002/rsa.20573

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We study the cover time of a random graph chosen uniformly at random from the set of graphs with vertex set [n] and degree sequence. In a previous work (Abdullah, Cooper, and Frieze, Discrete Math 312 (2012), 3146-3163), the asymptotic cover time was obtained under a number of assumptions on d, the most significant being that d(i) 3 for all i. Here we replace this assumption by d(i) 2. As a corollary, we establish the asymptotic cover time for the 2-core of the emerging giant component of G(n,p). (c) 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 627-674, 2014

引用

页码：627 / 674

页数：48

共 50 条

[31] THE DISTRIBUTION OF THE MAXIMUM DEGREE OF A RANDOM GRAPH
BOLLOBAS, B
DISCRETE MATHEMATICS, 1980, 32 (02) : 201 - 203
[32] Spectral radius and degree sequence of a graph
Liu, Chia-an
Weng, Chih-wen
LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (08) : 3511 - 3515
[33] RADIUS, DIAMETER AND THE DEGREE SEQUENCE OF A GRAPH
Mazorodze, Jaya Percival
Mukwembi, Simon
MATHEMATICA SLOVACA, 2015, 65 (06) : 1223 - 1236
[34] DEGREE SEQUENCE OF THE GENERALIZED SIERPISKI GRAPH
Khatibi, Mahsa
Behtoei, Ali
Attarzadeh, Fatemeh
CONTRIBUTIONS TO DISCRETE MATHEMATICS, 2020, 15 (03) : 88 - 97
[35] Graph Editing to a Given Degree Sequence
Golovach, Petr A.
Mertzios, George B.
COMPUTER SCIENCE - THEORY AND APPLICATIONS, CSR 2016, 2016, 9691 : 177 - 191
[36] Graph editing to a given degree sequence
Golovach, Petr A.
Mertzios, George B.
THEORETICAL COMPUTER SCIENCE, 2017, 665 : 1 - 12
[37] A note on diameter and the degree sequence of a graph
Mukwembi, Simon
APPLIED MATHEMATICS LETTERS, 2012, 25 (02) : 175 - 178
[38] THE NUMBER OF CUT-VERTICES IN A GRAPH OF GIVEN MINIMUM DEGREE
ALBERTSON, MO
BERMAN, DM
DISCRETE MATHEMATICS, 1991, 89 (01) : 97 - 100
[39] How to determine if a random graph with a fixed degree sequence has a giant component
Joos, Felix
Perarnau, Guillem
Rautenbach, Dieter
Reed, Bruce
PROBABILITY THEORY AND RELATED FIELDS, 2018, 170 (1-2) : 263 - 310
[40] Phase transition on the degree sequence of a random graph process with vertex copying and deletion
Cai, Kai-Yuan
Dong, Zhao
Liu, Ke
Wu, Xian-Yuan
STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2011, 121 (04) : 885 - 895

← 1 2 3 4 5 →