A note on long cycles in sparse random graphs
Anastos M. 2023. A note on long cycles in sparse random graphs. Electronic Journal of Combinatorics. 30(2), P2.21.
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Abstract
Let Lc,n denote the size of the longest cycle in G(n, c/n),c >1 constant. We show that there exists a continuous function f(c) such that Lc,n/n→f(c) a.s. for c>20, thus extending a result of Frieze and the author to smaller values of c. Thereafter, for c>20, we determine the limit of the probability that G(n, c/n)contains cycles of every length between the length of its shortest and its longest cycles as n→∞.
Publishing Year
Date Published
2023-05-05
Journal Title
Electronic Journal of Combinatorics
Acknowledgement
We would like to thank the reviewers for their helpful comments and remarks.
Volume
30
Issue
2
Article Number
P2.21
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IST-REx-ID
Cite this
Anastos M. A note on long cycles in sparse random graphs. Electronic Journal of Combinatorics. 2023;30(2). doi:10.37236/11471
Anastos, M. (2023). A note on long cycles in sparse random graphs. Electronic Journal of Combinatorics. Electronic Journal of Combinatorics. https://doi.org/10.37236/11471
Anastos, Michael. “A Note on Long Cycles in Sparse Random Graphs.” Electronic Journal of Combinatorics. Electronic Journal of Combinatorics, 2023. https://doi.org/10.37236/11471.
M. Anastos, “A note on long cycles in sparse random graphs,” Electronic Journal of Combinatorics, vol. 30, no. 2. Electronic Journal of Combinatorics, 2023.
Anastos M. 2023. A note on long cycles in sparse random graphs. Electronic Journal of Combinatorics. 30(2), P2.21.
Anastos, Michael. “A Note on Long Cycles in Sparse Random Graphs.” Electronic Journal of Combinatorics, vol. 30, no. 2, P2.21, Electronic Journal of Combinatorics, 2023, doi:10.37236/11471.
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