Finding Hamilton cycles in random intersection graphs

The construction of the random intersection graph model is based on a random family of sets. Such structures, which are derived from intersections of sets, appear in a natural manner in many applications. In this article we study the problem of finding a Hamilton cycle in a random intersection graph...

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Bibliographic Details
Published in:Discrete Mathematics and Theoretical Computer Science Vol. 20; no. 1; p. 1
Main Author: Rybarczyk, Katarzyna
Format: Journal Article
Language:English
Published: DMTCS 01.05.2018
Subjects:
Algorithms
Graph theory
Hamiltonian function
Mathematical research
Poland
ISSN:1462-7264
Online Access:Get full text
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Summary:The construction of the random intersection graph model is based on a random family of sets. Such structures, which are derived from intersections of sets, appear in a natural manner in many applications. In this article we study the problem of finding a Hamilton cycle in a random intersection graph. To this end we analyse a classical algorithm for finding Hamilton cycles in random graphs (algorithm HAM) and study its efficiency on graphs from a family of random intersection graphs (denoted here by G (n, m, p)). We prove that the threshold function for the property of HAM constructing a Hamilton cycle in G (n,m,p) is the same as the threshold function for the minimum degree at least two. Until now, known algorithms for finding Hamilton cycles in G (n,m,p) were designed to work in very small ranges of parameters and, unlike HAM, used the structure of the family of random sets. Keywords: random intersection graphs, Hamilton cycle, algorithm
ISSN:1462-7264