Long paths and connectivity in 1-independent random graphs

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14330%2F20%3A00118537" target="_blank" >RIV/00216224:14330/20:00118537 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1002/rsa.20972" target="_blank" >https://doi.org/10.1002/rsa.20972</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/rsa.20972" target="_blank" >10.1002/rsa.20972</a>

Result language

angličtina

Original language name

Long paths and connectivity in 1-independent random graphs

Original language description

A probability measure.. on the subsets of the edge set of a graph G is a 1-independent probability measure (1-ipm) on G if events determined by edge sets that are at graph distance at least 1 apart in G are independent. Given a 1-ipm denote by G.. the associated random graph model. Let. 1,.p(G) denote the collection of 1-ipms.. onGforwhich each edge is included inG.. with probability at least p. For G = Z2, Balister and Bollobas asked for the value of the least p. such that for all p &gt; p. and al mu epsilon M1 &gt;= p(G)(mu) (G).. almost surely contains an infinite component. In this paper, we significantly improve previous lower bounds on p.. We also determine the 1-independent critical probability for the emergence of long paths on the line and ladder lattices. Finally, for finite graphs G we study f 1,G(p), the infimum over all mu epsilon M (1)&gt;=(p)(G) of the probability that G.. is connected. We determine f 1,G(p) exactly when G is a path, a complete graph and a cycle of length at most 5.

Czech name

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Czech description

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Type

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

CEP classification

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OECD FORD branch

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

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

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

Name of the periodical

Random Structures & Algorithms

ISSN

1042-9832

e-ISSN

—

Volume of the periodical

57

Issue of the periodical within the volume

4

Country of publishing house

US - UNITED STATES

Number of pages

43

Pages from-to

1007-1049

UT code for WoS article

000577434000001

EID of the result in the Scopus database

2-s2.0-85092609413