The Erdös-Jacobson-Lehel conjecture on potentiallyPk-graphic sequence is true

The Erdös-Jacobson-Lehel conjecture on potentiallyPk-graphic sequence is true

A variation in the classical Turan extrernal problem is studied. A simple graphG of ordern is said to have propertyPk if it contains a clique of sizek+1 as its subgraph. Ann-term nonincreasing nonnegative integer sequence π=(d1, d2,⋯, d2) is said to be graphic if it is the degree sequence of a simpl...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Science China. Mathematics 1998-01, Vol.41 (5), p.510-520
Hauptverfasser: Li Jiongsheng, Song Zixia, Luo Rong
Format: Artikel
Sprache:eng
Schlagworte:
Graph theory
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 520
container_issue 5
container_start_page 510
container_title Science China. Mathematics
container_volume 41
creator Li Jiongsheng
Song Zixia
Luo Rong
description A variation in the classical Turan extrernal problem is studied. A simple graphG of ordern is said to have propertyPk if it contains a clique of sizek+1 as its subgraph. Ann-term nonincreasing nonnegative integer sequence π=(d1, d2,⋯, d2) is said to be graphic if it is the degree sequence of a simple graphG of ordern and such a graphG is referred to as a realization of π. A graphic sequence π is said to be potentiallyPk-graphic if it has a realizationG having propertyPk. The problem: determine the smallest positive even number σ(k, n) such that everyn-term graphic sequence π=(d1, d2,…, d2) without zero terms and with degree sum σ(π)=(d1+d2+ …+d2) at least σ(k,n) is potentially Pk-graphic has been proved positive.
doi_str_mv 10.1007/BF02879940
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_2786948309</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2786948309</sourcerecordid><originalsourceid>FETCH-proquest_journals_27869483093</originalsourceid><addsrcrecordid>eNqNjrEKwjAYhIMoWLSLTxBwjqZNaZpVqYiIOHQvNf7a1pLUJB18MV_AFzODD-ANdwf3DYfQIqKriFK-3uxonHEhEjpCQZSlgniLx76nPCE8ztgUhda21IsJmnAWoFNRA87N9fO25FBJfbFakSPU0GGpVQvSDQawVrjXDpRrqq57nR_kbqq-biS28BxAScCNxc4MMEeTW9VZCH85Q8tdXmz3pDfak9aVrR6M8lMZc_8wyRgV7D_qCyxYRPA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2786948309</pqid></control><display><type>article</type><title>The Erdös-Jacobson-Lehel conjecture on potentiallyPk-graphic sequence is true</title><source>SpringerLink (Online service)</source><source>Alma/SFX Local Collection</source><creator>Li Jiongsheng ; Song Zixia ; Luo Rong</creator><creatorcontrib>Li Jiongsheng ; Song Zixia ; Luo Rong</creatorcontrib><description>A variation in the classical Turan extrernal problem is studied. A simple graphG of ordern is said to have propertyPk if it contains a clique of sizek+1 as its subgraph. Ann-term nonincreasing nonnegative integer sequence π=(d1, d2,⋯, d2) is said to be graphic if it is the degree sequence of a simple graphG of ordern and such a graphG is referred to as a realization of π. A graphic sequence π is said to be potentiallyPk-graphic if it has a realizationG having propertyPk. The problem: determine the smallest positive even number σ(k, n) such that everyn-term graphic sequence π=(d1, d2,…, d2) without zero terms and with degree sum σ(π)=(d1+d2+ …+d2) at least σ(k,n) is potentially Pk-graphic has been proved positive.</description><identifier>ISSN: 1674-7283</identifier><identifier>EISSN: 1869-1862</identifier><identifier>DOI: 10.1007/BF02879940</identifier><language>eng</language><publisher>Heidelberg: Springer Nature B.V</publisher><subject>Graph theory</subject><ispartof>Science China. Mathematics, 1998-01, Vol.41 (5), p.510-520</ispartof><rights>Science in China Press 1998.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><creatorcontrib>Li Jiongsheng</creatorcontrib><creatorcontrib>Song Zixia</creatorcontrib><creatorcontrib>Luo Rong</creatorcontrib><title>The Erdös-Jacobson-Lehel conjecture on potentiallyPk-graphic sequence is true</title><title>Science China. Mathematics</title><description>A variation in the classical Turan extrernal problem is studied. A simple graphG of ordern is said to have propertyPk if it contains a clique of sizek+1 as its subgraph. Ann-term nonincreasing nonnegative integer sequence π=(d1, d2,⋯, d2) is said to be graphic if it is the degree sequence of a simple graphG of ordern and such a graphG is referred to as a realization of π. A graphic sequence π is said to be potentiallyPk-graphic if it has a realizationG having propertyPk. The problem: determine the smallest positive even number σ(k, n) such that everyn-term graphic sequence π=(d1, d2,…, d2) without zero terms and with degree sum σ(π)=(d1+d2+ …+d2) at least σ(k,n) is potentially Pk-graphic has been proved positive.</description><subject>Graph theory</subject><issn>1674-7283</issn><issn>1869-1862</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1998</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNqNjrEKwjAYhIMoWLSLTxBwjqZNaZpVqYiIOHQvNf7a1pLUJB18MV_AFzODD-ANdwf3DYfQIqKriFK-3uxonHEhEjpCQZSlgniLx76nPCE8ztgUhda21IsJmnAWoFNRA87N9fO25FBJfbFakSPU0GGpVQvSDQawVrjXDpRrqq57nR_kbqq-biS28BxAScCNxc4MMEeTW9VZCH85Q8tdXmz3pDfak9aVrR6M8lMZc_8wyRgV7D_qCyxYRPA</recordid><startdate>19980101</startdate><enddate>19980101</enddate><creator>Li Jiongsheng</creator><creator>Song Zixia</creator><creator>Luo Rong</creator><general>Springer Nature B.V</general><scope/></search><sort><creationdate>19980101</creationdate><title>The Erdös-Jacobson-Lehel conjecture on potentiallyPk-graphic sequence is true</title><author>Li Jiongsheng ; Song Zixia ; Luo Rong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_27869483093</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1998</creationdate><topic>Graph theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li Jiongsheng</creatorcontrib><creatorcontrib>Song Zixia</creatorcontrib><creatorcontrib>Luo Rong</creatorcontrib><jtitle>Science China. Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li Jiongsheng</au><au>Song Zixia</au><au>Luo Rong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Erdös-Jacobson-Lehel conjecture on potentiallyPk-graphic sequence is true</atitle><jtitle>Science China. Mathematics</jtitle><date>1998-01-01</date><risdate>1998</risdate><volume>41</volume><issue>5</issue><spage>510</spage><epage>520</epage><pages>510-520</pages><issn>1674-7283</issn><eissn>1869-1862</eissn><abstract>A variation in the classical Turan extrernal problem is studied. A simple graphG of ordern is said to have propertyPk if it contains a clique of sizek+1 as its subgraph. Ann-term nonincreasing nonnegative integer sequence π=(d1, d2,⋯, d2) is said to be graphic if it is the degree sequence of a simple graphG of ordern and such a graphG is referred to as a realization of π. A graphic sequence π is said to be potentiallyPk-graphic if it has a realizationG having propertyPk. The problem: determine the smallest positive even number σ(k, n) such that everyn-term graphic sequence π=(d1, d2,…, d2) without zero terms and with degree sum σ(π)=(d1+d2+ …+d2) at least σ(k,n) is potentially Pk-graphic has been proved positive.</abstract><cop>Heidelberg</cop><pub>Springer Nature B.V</pub><doi>10.1007/BF02879940</doi></addata></record>
fulltext fulltext
identifier ISSN: 1674-7283
ispartof Science China. Mathematics, 1998-01, Vol.41 (5), p.510-520
issn 1674-7283
1869-1862
language eng
recordid cdi_proquest_journals_2786948309
source SpringerLink (Online service); Alma/SFX Local Collection
subjects Graph theory
title The Erdös-Jacobson-Lehel conjecture on potentiallyPk-graphic sequence is true
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-27T21%3A31%3A47IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20Erd%C3%B6s-Jacobson-Lehel%20conjecture%20on%20potentiallyPk-graphic%20sequence%20is%20true&rft.jtitle=Science%20China.%20Mathematics&rft.au=Li%20Jiongsheng&rft.date=1998-01-01&rft.volume=41&rft.issue=5&rft.spage=510&rft.epage=520&rft.pages=510-520&rft.issn=1674-7283&rft.eissn=1869-1862&rft_id=info:doi/10.1007/BF02879940&rft_dat=%3Cproquest%3E2786948309%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2786948309&rft_id=info:pmid/&rfr_iscdi=true