Random regular graphs of high degree

Michael Krivelevich; Benny Sudakov; Van H. Vu; Nicholas C. Wormald

doi:10.1002/rsa.1013

Random regular graphs of high degree

Michael Krivelevich^*
, Benny Sudakov
, Van H. Vu
, Nicholas C. Wormald

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

72 Scopus citations

Abstract

Random d-regular graphs have been well studied when d is fixed and the number of vertices goes to infinity. We obtain results on many of the properties of a random d-regular graph when d = d(n) grows more quickly than √n. These properties include connectivity, hamiltonicity, independent set size, chromatic number, choice number, and the size of the second eigenvalue, among others.

Original language	English
Pages (from-to)	346-363
Number of pages	18
Journal	Random Structures and Algorithms
Volume	18
Issue number	4
DOIs	https://doi.org/10.1002/rsa.1013
State	Published - Jul 2001

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10.1002/rsa.1013

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title = "Random regular graphs of high degree",

abstract = "Random d-regular graphs have been well studied when d is fixed and the number of vertices goes to infinity. We obtain results on many of the properties of a random d-regular graph when d = d(n) grows more quickly than √n. These properties include connectivity, hamiltonicity, independent set size, chromatic number, choice number, and the size of the second eigenvalue, among others.",

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year = "2001",

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N2 - Random d-regular graphs have been well studied when d is fixed and the number of vertices goes to infinity. We obtain results on many of the properties of a random d-regular graph when d = d(n) grows more quickly than √n. These properties include connectivity, hamiltonicity, independent set size, chromatic number, choice number, and the size of the second eigenvalue, among others.

AB - Random d-regular graphs have been well studied when d is fixed and the number of vertices goes to infinity. We obtain results on many of the properties of a random d-regular graph when d = d(n) grows more quickly than √n. These properties include connectivity, hamiltonicity, independent set size, chromatic number, choice number, and the size of the second eigenvalue, among others.

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Random regular graphs of high degree

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