An almost linear time algorithm for finding Hamilton cycles in sparse random graphs with minimum degree at least three

Alan Frieze; Simi Haber

doi:https://doi.org/10.1002/rsa.20542

An almost linear time algorithm for finding Hamilton cycles in sparse random graphs with minimum degree at least three

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

Abstract

We describe an algorithm for finding Hamilton cycles in random graphs. Our model is the random graph G=G_n,mδ≥3. In this model G is drawn uniformly from graphs with vertex set [n], m edges and minimum degree at least three. We focus on the case where m = cn for constant c. If c is sufficiently large then our algorithm runs in O(n^1+o(1)) time and succeeds w.h.p.

Original language	English
Pages (from-to)	73-98
Number of pages	26
Journal	Random Structures and Algorithms
Volume	47
Issue number	1
DOIs	https://doi.org/10.1002/rsa.20542
State	Published - 1 Aug 2015
Externally published	Yes

Keywords

Fast algorithm
Hamilton cycles
Random graphs

All Science Journal Classification (ASJC) codes

Software
Applied Mathematics
General Mathematics
Computer Graphics and Computer-Aided Design

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https://doi.org/10.1002/rsa.20542

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title = "An almost linear time algorithm for finding Hamilton cycles in sparse random graphs with minimum degree at least three",

abstract = "We describe an algorithm for finding Hamilton cycles in random graphs. Our model is the random graph G=Gn,mδ≥3. In this model G is drawn uniformly from graphs with vertex set [n], m edges and minimum degree at least three. We focus on the case where m = cn for constant c. If c is sufficiently large then our algorithm runs in O(n1+o(1)) time and succeeds w.h.p.",

keywords = "Fast algorithm, Hamilton cycles, Random graphs",

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doi = "https://doi.org/10.1002/rsa.20542",

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AU - Haber, Simi

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N2 - We describe an algorithm for finding Hamilton cycles in random graphs. Our model is the random graph G=Gn,mδ≥3. In this model G is drawn uniformly from graphs with vertex set [n], m edges and minimum degree at least three. We focus on the case where m = cn for constant c. If c is sufficiently large then our algorithm runs in O(n1+o(1)) time and succeeds w.h.p.

AB - We describe an algorithm for finding Hamilton cycles in random graphs. Our model is the random graph G=Gn,mδ≥3. In this model G is drawn uniformly from graphs with vertex set [n], m edges and minimum degree at least three. We focus on the case where m = cn for constant c. If c is sufficiently large then our algorithm runs in O(n1+o(1)) time and succeeds w.h.p.

KW - Fast algorithm

KW - Hamilton cycles

KW - Random graphs

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DO - https://doi.org/10.1002/rsa.20542

M3 - مقالة

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ER -

An almost linear time algorithm for finding Hamilton cycles in sparse random graphs with minimum degree at least three

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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