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

Alan Frieze; Simi Haber

doi:10.1002/rsa.20542

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

Alan Frieze
, Simi Haber

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

ASJC Scopus subject areas

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

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10.1002/rsa.20542

Cite this

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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.",

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

Abstract

Keywords

ASJC Scopus subject areas

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