Spanning structures and universality in sparse hypergraphs

In this paper the problem of finding various spanning structures in random hypergraphs is studied. We notice that a general result of Riordan [Combin Probab Comput 9 (2000), 125–148] can be adapted from random graphs to random r‐uniform hypergraphs and provide sufficient conditions when a random r‐u...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Random structures & algorithms 2016-12, Vol.49 (4), p.819-844
Hauptverfasser: Parczyk, Olaf, Person, Yury
Format: Artikel
Sprache:eng
Schlagworte:
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 844
container_issue 4
container_start_page 819
container_title Random structures & algorithms
container_volume 49
creator Parczyk, Olaf
Person, Yury
description In this paper the problem of finding various spanning structures in random hypergraphs is studied. We notice that a general result of Riordan [Combin Probab Comput 9 (2000), 125–148] can be adapted from random graphs to random r‐uniform hypergraphs and provide sufficient conditions when a random r‐uniform hypergraph H(r)(n,p) contains a given spanning structure a.a.s. We also discuss several spanning structures such as cube‐hypergraphs, lattices, spheres, and Hamilton cycles in hypergraphs. Moreover, we study universality, i.e. when does an r‐uniform hypergraph contain any hypergraph on n vertices and with maximum vertex degree bounded by Δ? For H(r)(n,p) it is shown that this holds for p≫(lnn/n)1/Δ a.a.s. by combining approaches taken by Dellamonica, Kohayakawa, Rödl and Ruciński [Random Struct Algorithms 46 (2015), 274–299] and of Ferber, Nenadov and Peter [Random Struct Algorithms 48 (2016), 546–564] and of Kim and Lee [SIAM J Discrete Math 28 (2014), 1467–1478]. Furthermore it is shown that the random graph G(n, p) for appropriate p and explicit constructions of universal graphs due to Alon, Capalbo, Kohayakawa, Rödl, Ruciński and Szemerédi [Lecture Notes in Comput. Sci., Vol. 2129, Springer, Berlin, 2001, pp. 170–180] and Alon and Capalbo [Random Struct Algorithms 31 (2007), 123–133; Proceedings of the 9th Annual ACM‐SIAM Symposium Society of Industrial and Applied Mathematics, 2008, pp. 373–378] yield constructions of universal hypergraphs that are sparser than the random hypergraph H(r)(n,p) with p≫(lnn/n)1/Δ © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 819–844, 2016
doi_str_mv 10.1002/rsa.20690
format Article
fullrecord <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1855365796</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>4226399381</sourcerecordid><originalsourceid>FETCH-LOGICAL-c4030-72e83c94455a95d128784eef95121141bb951722de2c3f9e4865b47c209d940c3</originalsourceid><addsrcrecordid>eNp10D1PwzAQBuAIgUQpDPyDSCwwpPVnbLNViBZQBYiCGC03cVqX1A12AuTf4xJgQGK6G573dHdRdAzBAAKAhs6rAQKpADtRDwLBE0Qg3932BCWCY7QfHXi_AgAwjHAvOp9VylpjF7GvXZPVjdM-VjaPG2vedJhWmrqNjY19pZzX8bKttFs4VS39YbRXqNLro-_aj57Gl48XV8n0bnJ9MZomGQEYJAxpjjNBCKVK0BwizjjRuhAUIggJnM9DxxDKNcpwITThKZ0TliEgckFAhvvRaTe3cpvXRvtaro3PdFkqqzeNl5BTilPKRBroyR-62jTOhu2CwpClHAMY1FmnMrfx3ulCVs6slWslBHL7RRnull9fDHbY2XdT6vZ_KB9mo59E0iWMr_XHb0K5F5kyzKh8vp1IdIPEZMrG8h5_AvKcgLo</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1831768301</pqid></control><display><type>article</type><title>Spanning structures and universality in sparse hypergraphs</title><source>Wiley Online Library Journals Frontfile Complete</source><creator>Parczyk, Olaf ; Person, Yury</creator><creatorcontrib>Parczyk, Olaf ; Person, Yury</creatorcontrib><description>In this paper the problem of finding various spanning structures in random hypergraphs is studied. We notice that a general result of Riordan [Combin Probab Comput 9 (2000), 125–148] can be adapted from random graphs to random r‐uniform hypergraphs and provide sufficient conditions when a random r‐uniform hypergraph H(r)(n,p) contains a given spanning structure a.a.s. We also discuss several spanning structures such as cube‐hypergraphs, lattices, spheres, and Hamilton cycles in hypergraphs. Moreover, we study universality, i.e. when does an r‐uniform hypergraph contain any hypergraph on n vertices and with maximum vertex degree bounded by Δ? For H(r)(n,p) it is shown that this holds for p≫(lnn/n)1/Δ a.a.s. by combining approaches taken by Dellamonica, Kohayakawa, Rödl and Ruciński [Random Struct Algorithms 46 (2015), 274–299] and of Ferber, Nenadov and Peter [Random Struct Algorithms 48 (2016), 546–564] and of Kim and Lee [SIAM J Discrete Math 28 (2014), 1467–1478]. Furthermore it is shown that the random graph G(n, p) for appropriate p and explicit constructions of universal graphs due to Alon, Capalbo, Kohayakawa, Rödl, Ruciński and Szemerédi [Lecture Notes in Comput. Sci., Vol. 2129, Springer, Berlin, 2001, pp. 170–180] and Alon and Capalbo [Random Struct Algorithms 31 (2007), 123–133; Proceedings of the 9th Annual ACM‐SIAM Symposium Society of Industrial and Applied Mathematics, 2008, pp. 373–378] yield constructions of universal hypergraphs that are sparser than the random hypergraph H(r)(n,p) with p≫(lnn/n)1/Δ © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 819–844, 2016</description><identifier>ISSN: 1042-9832</identifier><identifier>EISSN: 1098-2418</identifier><identifier>DOI: 10.1002/rsa.20690</identifier><language>eng</language><publisher>Hoboken: Blackwell Publishing Ltd</publisher><subject>Algorithms ; Construction ; Construction industry ; Graphs ; Lattices ; Lectures ; Mathematical models ; random hypergraphs ; spanning structures ; thresholds ; universality</subject><ispartof>Random structures &amp; algorithms, 2016-12, Vol.49 (4), p.819-844</ispartof><rights>2016 Wiley Periodicals, Inc.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c4030-72e83c94455a95d128784eef95121141bb951722de2c3f9e4865b47c209d940c3</citedby><cites>FETCH-LOGICAL-c4030-72e83c94455a95d128784eef95121141bb951722de2c3f9e4865b47c209d940c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Frsa.20690$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Frsa.20690$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,777,781,1412,27905,27906,45555,45556</link.rule.ids></links><search><creatorcontrib>Parczyk, Olaf</creatorcontrib><creatorcontrib>Person, Yury</creatorcontrib><title>Spanning structures and universality in sparse hypergraphs</title><title>Random structures &amp; algorithms</title><addtitle>Random Struct. Alg</addtitle><description>In this paper the problem of finding various spanning structures in random hypergraphs is studied. We notice that a general result of Riordan [Combin Probab Comput 9 (2000), 125–148] can be adapted from random graphs to random r‐uniform hypergraphs and provide sufficient conditions when a random r‐uniform hypergraph H(r)(n,p) contains a given spanning structure a.a.s. We also discuss several spanning structures such as cube‐hypergraphs, lattices, spheres, and Hamilton cycles in hypergraphs. Moreover, we study universality, i.e. when does an r‐uniform hypergraph contain any hypergraph on n vertices and with maximum vertex degree bounded by Δ? For H(r)(n,p) it is shown that this holds for p≫(lnn/n)1/Δ a.a.s. by combining approaches taken by Dellamonica, Kohayakawa, Rödl and Ruciński [Random Struct Algorithms 46 (2015), 274–299] and of Ferber, Nenadov and Peter [Random Struct Algorithms 48 (2016), 546–564] and of Kim and Lee [SIAM J Discrete Math 28 (2014), 1467–1478]. Furthermore it is shown that the random graph G(n, p) for appropriate p and explicit constructions of universal graphs due to Alon, Capalbo, Kohayakawa, Rödl, Ruciński and Szemerédi [Lecture Notes in Comput. Sci., Vol. 2129, Springer, Berlin, 2001, pp. 170–180] and Alon and Capalbo [Random Struct Algorithms 31 (2007), 123–133; Proceedings of the 9th Annual ACM‐SIAM Symposium Society of Industrial and Applied Mathematics, 2008, pp. 373–378] yield constructions of universal hypergraphs that are sparser than the random hypergraph H(r)(n,p) with p≫(lnn/n)1/Δ © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 819–844, 2016</description><subject>Algorithms</subject><subject>Construction</subject><subject>Construction industry</subject><subject>Graphs</subject><subject>Lattices</subject><subject>Lectures</subject><subject>Mathematical models</subject><subject>random hypergraphs</subject><subject>spanning structures</subject><subject>thresholds</subject><subject>universality</subject><issn>1042-9832</issn><issn>1098-2418</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp10D1PwzAQBuAIgUQpDPyDSCwwpPVnbLNViBZQBYiCGC03cVqX1A12AuTf4xJgQGK6G573dHdRdAzBAAKAhs6rAQKpADtRDwLBE0Qg3932BCWCY7QfHXi_AgAwjHAvOp9VylpjF7GvXZPVjdM-VjaPG2vedJhWmrqNjY19pZzX8bKttFs4VS39YbRXqNLro-_aj57Gl48XV8n0bnJ9MZomGQEYJAxpjjNBCKVK0BwizjjRuhAUIggJnM9DxxDKNcpwITThKZ0TliEgckFAhvvRaTe3cpvXRvtaro3PdFkqqzeNl5BTilPKRBroyR-62jTOhu2CwpClHAMY1FmnMrfx3ulCVs6slWslBHL7RRnull9fDHbY2XdT6vZ_KB9mo59E0iWMr_XHb0K5F5kyzKh8vp1IdIPEZMrG8h5_AvKcgLo</recordid><startdate>201612</startdate><enddate>201612</enddate><creator>Parczyk, Olaf</creator><creator>Person, Yury</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201612</creationdate><title>Spanning structures and universality in sparse hypergraphs</title><author>Parczyk, Olaf ; Person, Yury</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4030-72e83c94455a95d128784eef95121141bb951722de2c3f9e4865b47c209d940c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Algorithms</topic><topic>Construction</topic><topic>Construction industry</topic><topic>Graphs</topic><topic>Lattices</topic><topic>Lectures</topic><topic>Mathematical models</topic><topic>random hypergraphs</topic><topic>spanning structures</topic><topic>thresholds</topic><topic>universality</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Parczyk, Olaf</creatorcontrib><creatorcontrib>Person, Yury</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Random structures &amp; algorithms</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Parczyk, Olaf</au><au>Person, Yury</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Spanning structures and universality in sparse hypergraphs</atitle><jtitle>Random structures &amp; algorithms</jtitle><addtitle>Random Struct. Alg</addtitle><date>2016-12</date><risdate>2016</risdate><volume>49</volume><issue>4</issue><spage>819</spage><epage>844</epage><pages>819-844</pages><issn>1042-9832</issn><eissn>1098-2418</eissn><abstract>In this paper the problem of finding various spanning structures in random hypergraphs is studied. We notice that a general result of Riordan [Combin Probab Comput 9 (2000), 125–148] can be adapted from random graphs to random r‐uniform hypergraphs and provide sufficient conditions when a random r‐uniform hypergraph H(r)(n,p) contains a given spanning structure a.a.s. We also discuss several spanning structures such as cube‐hypergraphs, lattices, spheres, and Hamilton cycles in hypergraphs. Moreover, we study universality, i.e. when does an r‐uniform hypergraph contain any hypergraph on n vertices and with maximum vertex degree bounded by Δ? For H(r)(n,p) it is shown that this holds for p≫(lnn/n)1/Δ a.a.s. by combining approaches taken by Dellamonica, Kohayakawa, Rödl and Ruciński [Random Struct Algorithms 46 (2015), 274–299] and of Ferber, Nenadov and Peter [Random Struct Algorithms 48 (2016), 546–564] and of Kim and Lee [SIAM J Discrete Math 28 (2014), 1467–1478]. Furthermore it is shown that the random graph G(n, p) for appropriate p and explicit constructions of universal graphs due to Alon, Capalbo, Kohayakawa, Rödl, Ruciński and Szemerédi [Lecture Notes in Comput. Sci., Vol. 2129, Springer, Berlin, 2001, pp. 170–180] and Alon and Capalbo [Random Struct Algorithms 31 (2007), 123–133; Proceedings of the 9th Annual ACM‐SIAM Symposium Society of Industrial and Applied Mathematics, 2008, pp. 373–378] yield constructions of universal hypergraphs that are sparser than the random hypergraph H(r)(n,p) with p≫(lnn/n)1/Δ © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 819–844, 2016</abstract><cop>Hoboken</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/rsa.20690</doi><tpages>26</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1042-9832
ispartof Random structures & algorithms, 2016-12, Vol.49 (4), p.819-844
issn 1042-9832
1098-2418
language eng
recordid cdi_proquest_miscellaneous_1855365796
source Wiley Online Library Journals Frontfile Complete
subjects Algorithms
Construction
Construction industry
Graphs
Lattices
Lectures
Mathematical models
random hypergraphs
spanning structures
thresholds
universality
title Spanning structures and universality in sparse hypergraphs
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-18T09%3A48%3A20IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Spanning%20structures%20and%20universality%20in%20sparse%20hypergraphs&rft.jtitle=Random%20structures%20&%20algorithms&rft.au=Parczyk,%20Olaf&rft.date=2016-12&rft.volume=49&rft.issue=4&rft.spage=819&rft.epage=844&rft.pages=819-844&rft.issn=1042-9832&rft.eissn=1098-2418&rft_id=info:doi/10.1002/rsa.20690&rft_dat=%3Cproquest_cross%3E4226399381%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1831768301&rft_id=info:pmid/&rfr_iscdi=true