Random perturbation of sparse graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F21%3A00125244" target="_blank" >RIV/00216224:14330/21:00125244 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.37236/9510" target="_blank" >https://doi.org/10.37236/9510</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.37236/9510" target="_blank" >10.37236/9510</a>

Result language

angličtina

Original language name

Random perturbation of sparse graphs

Original language description

In the model of randomly perturbed graphs we consider the union of a deterministic graph G α with minimum degree α n and the binomial random graph G ( n , p ) . This model was introduced by Bohman, Frieze, and Martin and for Hamilton cycles their result bridges the gap between Dirac's theorem and the results by Pósa and Korshunov on the threshold in G ( n , p ) . In this note we extend this result in G α ∪ G ( n , p ) to sparser graphs with α = o ( 1 ) . More precisely, for any ε &gt; 0 and α : N ↦ ( 0 , 1 ) we show that a.a.s. G α ∪ G ( n , β / n ) is Hamiltonian, where β = − ( 6 + ε ) log ( α ) . If α &gt; 0 is a fixed constant this gives the aforementioned result by Bohman, Frieze, and Martin and if α = O ( 1 / n ) the random part G ( n , p ) is sufficient for a Hamilton cycle. We also discuss embeddings of bounded degree trees and other spanning structures in this model, which lead to interesting questions on almost spanning embeddings into G ( n , p ) .

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2021

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Electronic Journal of Combinatorics

ISSN

1077-8926

e-ISSN

—

Volume of the periodical

28

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

12

Pages from-to

1-12

UT code for WoS article

000762018300001

EID of the result in the Scopus database

2-s2.0-85106001723