The bisection width of cubic graphs

The bisection width of cubic graphs

For a graph G, define the bisection width bw(G) of G as min { eG(A,B): {A,B} partitions V(G) with ‖A| − |B‖ ≤ 1 } where eG(A, B) denotes the number of edges in G with one end in A and one end in B. We show almost every cubic graph G of order n has bw(G) ≥ n/11 while every such graph has bw(G) ≤ (n +...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Bulletin of the Australian Mathematical Society 1989-06, Vol.39 (3), p.389-396
Hauptverfasser: Clark, L.H., Entringer, R.C.
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page 396
container_issue 3
container_start_page 389
container_title Bulletin of the Australian Mathematical Society
container_volume 39
creator Clark, L.H.
Entringer, R.C.
description For a graph G, define the bisection width bw(G) of G as min { eG(A,B): {A,B} partitions V(G) with ‖A| − |B‖ ≤ 1 } where eG(A, B) denotes the number of edges in G with one end in A and one end in B. We show almost every cubic graph G of order n has bw(G) ≥ n/11 while every such graph has bw(G) ≤ (n + 138)/3. We also show that almost every r-regular graph G of order n has bw(G) ≥ crn where cr → r/4 as r → ∞. Our last result is asymtotically correct.
doi_str_mv 10.1017/S0004972700003300
format Article
fullrecord <record><control><sourceid>cambridge_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1017_S0004972700003300</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><cupid>10_1017_S0004972700003300</cupid><sourcerecordid>10_1017_S0004972700003300</sourcerecordid><originalsourceid>FETCH-LOGICAL-c399t-cc21309181467fc50349cf38684ad6ef984ab28e6e00c0226814691f76292fe33</originalsourceid><addsrcrecordid>eNp9j19LwzAUxYMoOKcfwLeCvlZvkjZpHnW4-Wcg4nwOaZpsmVtbkg7125vSsRfBp8Pl_M7lHIQuMdxgwPz2HQAywQmPCpQCHKER5nmeYkbpMRr1dtr7p-gshHW88pwUI3S1WJmkdMHozjV18uWqbpU0NtG70ulk6VW7CufoxKpNMBd7HaOP6cNi8pjOX2dPk7t5qqkQXao1wRQELnDGuNU50ExoSwtWZKpixoqoJSkMMwAaCGE9KLDljAhiDaVjhIe_2jcheGNl691W-R-JQfYr5Z-VMXM9ZFoVtNpYr2rtwiHIY4dM4IilA-ZCZ74PtvKfknHKc8lmb1K8zMnz7B6kiDzdV1Hb0rtqaeS62fk6zv-nzC82ZWxu</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>The bisection width of cubic graphs</title><source>CUP_剑桥大学出版社现刊</source><source>Free E-Journal (出版社公開部分のみ）</source><creator>Clark, L.H. ; Entringer, R.C.</creator><creatorcontrib>Clark, L.H. ; Entringer, R.C.</creatorcontrib><description>For a graph G, define the bisection width bw(G) of G as min { eG(A,B): {A,B} partitions V(G) with ‖A| − |B‖ ≤ 1 } where eG(A, B) denotes the number of edges in G with one end in A and one end in B. We show almost every cubic graph G of order n has bw(G) ≥ n/11 while every such graph has bw(G) ≤ (n + 138)/3. We also show that almost every r-regular graph G of order n has bw(G) ≥ crn where cr → r/4 as r → ∞. Our last result is asymtotically correct.</description><identifier>ISSN: 0004-9727</identifier><identifier>EISSN: 1755-1633</identifier><identifier>DOI: 10.1017/S0004972700003300</identifier><identifier>CODEN: ALNBAB</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Combinatorics ; Combinatorics. Ordered structures ; Exact sciences and technology ; Graph theory ; Mathematics ; Sciences and techniques of general use</subject><ispartof>Bulletin of the Australian Mathematical Society, 1989-06, Vol.39 (3), p.389-396</ispartof><rights>Copyright © Australian Mathematical Society 1989</rights><rights>1989 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c399t-cc21309181467fc50349cf38684ad6ef984ab28e6e00c0226814691f76292fe33</citedby><cites>FETCH-LOGICAL-c399t-cc21309181467fc50349cf38684ad6ef984ab28e6e00c0226814691f76292fe33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.cambridge.org/core/product/identifier/S0004972700003300/type/journal_article$$EHTML$$P50$$Gcambridge$$H</linktohtml><link.rule.ids>164,314,780,784,27924,27925,55628</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&amp;idt=7349491$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Clark, L.H.</creatorcontrib><creatorcontrib>Entringer, R.C.</creatorcontrib><title>The bisection width of cubic graphs</title><title>Bulletin of the Australian Mathematical Society</title><addtitle>Bull. Austral. Math. Soc</addtitle><description>For a graph G, define the bisection width bw(G) of G as min { eG(A,B): {A,B} partitions V(G) with ‖A| − |B‖ ≤ 1 } where eG(A, B) denotes the number of edges in G with one end in A and one end in B. We show almost every cubic graph G of order n has bw(G) ≥ n/11 while every such graph has bw(G) ≤ (n + 138)/3. We also show that almost every r-regular graph G of order n has bw(G) ≥ crn where cr → r/4 as r → ∞. Our last result is asymtotically correct.</description><subject>Combinatorics</subject><subject>Combinatorics. Ordered structures</subject><subject>Exact sciences and technology</subject><subject>Graph theory</subject><subject>Mathematics</subject><subject>Sciences and techniques of general use</subject><issn>0004-9727</issn><issn>1755-1633</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1989</creationdate><recordtype>article</recordtype><recordid>eNp9j19LwzAUxYMoOKcfwLeCvlZvkjZpHnW4-Wcg4nwOaZpsmVtbkg7125vSsRfBp8Pl_M7lHIQuMdxgwPz2HQAywQmPCpQCHKER5nmeYkbpMRr1dtr7p-gshHW88pwUI3S1WJmkdMHozjV18uWqbpU0NtG70ulk6VW7CufoxKpNMBd7HaOP6cNi8pjOX2dPk7t5qqkQXao1wRQELnDGuNU50ExoSwtWZKpixoqoJSkMMwAaCGE9KLDljAhiDaVjhIe_2jcheGNl691W-R-JQfYr5Z-VMXM9ZFoVtNpYr2rtwiHIY4dM4IilA-ZCZ74PtvKfknHKc8lmb1K8zMnz7B6kiDzdV1Hb0rtqaeS62fk6zv-nzC82ZWxu</recordid><startdate>19890601</startdate><enddate>19890601</enddate><creator>Clark, L.H.</creator><creator>Entringer, R.C.</creator><general>Cambridge University Press</general><general>University of Queensland Press</general><scope>BSCLL</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>19890601</creationdate><title>The bisection width of cubic graphs</title><author>Clark, L.H. ; Entringer, R.C.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c399t-cc21309181467fc50349cf38684ad6ef984ab28e6e00c0226814691f76292fe33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1989</creationdate><topic>Combinatorics</topic><topic>Combinatorics. Ordered structures</topic><topic>Exact sciences and technology</topic><topic>Graph theory</topic><topic>Mathematics</topic><topic>Sciences and techniques of general use</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Clark, L.H.</creatorcontrib><creatorcontrib>Entringer, R.C.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><jtitle>Bulletin of the Australian Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Clark, L.H.</au><au>Entringer, R.C.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The bisection width of cubic graphs</atitle><jtitle>Bulletin of the Australian Mathematical Society</jtitle><addtitle>Bull. Austral. Math. Soc</addtitle><date>1989-06-01</date><risdate>1989</risdate><volume>39</volume><issue>3</issue><spage>389</spage><epage>396</epage><pages>389-396</pages><issn>0004-9727</issn><eissn>1755-1633</eissn><coden>ALNBAB</coden><abstract>For a graph G, define the bisection width bw(G) of G as min { eG(A,B): {A,B} partitions V(G) with ‖A| − |B‖ ≤ 1 } where eG(A, B) denotes the number of edges in G with one end in A and one end in B. We show almost every cubic graph G of order n has bw(G) ≥ n/11 while every such graph has bw(G) ≤ (n + 138)/3. We also show that almost every r-regular graph G of order n has bw(G) ≥ crn where cr → r/4 as r → ∞. Our last result is asymtotically correct.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/S0004972700003300</doi><tpages>8</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0004-9727
ispartof Bulletin of the Australian Mathematical Society, 1989-06, Vol.39 (3), p.389-396
issn 0004-9727
1755-1633
language eng
recordid cdi_crossref_primary_10_1017_S0004972700003300
source CUP_剑桥大学出版社现刊; Free E-Journal (出版社公開部分のみ）
subjects Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Sciences and techniques of general use
title The bisection width of cubic graphs
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-01T08%3A21%3A10IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-cambridge_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20bisection%20width%20of%20cubic%20graphs&rft.jtitle=Bulletin%20of%20the%20Australian%20Mathematical%20Society&rft.au=Clark,%20L.H.&rft.date=1989-06-01&rft.volume=39&rft.issue=3&rft.spage=389&rft.epage=396&rft.pages=389-396&rft.issn=0004-9727&rft.eissn=1755-1633&rft.coden=ALNBAB&rft_id=info:doi/10.1017/S0004972700003300&rft_dat=%3Ccambridge_cross%3E10_1017_S0004972700003300%3C/cambridge_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rft_cupid=10_1017_S0004972700003300&rfr_iscdi=true