The weakly connected independent set polytope in corona and join of graphs
Given a connected undirected graph G = ( V , E ) , a subset W of nodes of G is a weakly connected independent set if W is an independent set and the partial graph ( V , δ ( W ) ) is connected, where δ ( W ) is the set of edges with only one endnode in W . This article proposes several distinct resul...
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| Veröffentlicht in: | Journal of combinatorial optimization 2018-10, Vol.36 (3), p.1007-1023 |
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| container_title | Journal of combinatorial optimization |
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| creator | Bendali, F. Mailfert, J. |
| description | Given a connected undirected graph
G
=
(
V
,
E
)
, a subset
W
of nodes of
G
is a weakly connected independent set if
W
is an independent set and the partial graph
(
V
,
δ
(
W
)
)
is connected, where
δ
(
W
)
is the set of edges with only one endnode in
W
. This article proposes several distinct results about the weakly connected independent sets of a graph obtained by corona or join operations: the complete description of the wcis polytope for a corona or a join of two graphs of which we know the wcis polytopes or the maximal independent set polytopes, and the consequences of these graph operations on the minimum weight weakly connected independent set problem (MWWCISP). A class of graphs is also inductively defined from the connected bipartite graphs, the cycles and the strongly chordal graphs, for which the MWWCISP is polynomially solvable. This work is a direct continuation of the article (Bendali et al. in Discrete Optim 22:87–110,
2016
) where a similar theorem about complete description of the wcis polytope has been given for 1-sum operation. |
| doi_str_mv | 10.1007/s10878-018-0275-9 |
| format | Article |
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G
=
(
V
,
E
)
, a subset
W
of nodes of
G
is a weakly connected independent set if
W
is an independent set and the partial graph
(
V
,
δ
(
W
)
)
is connected, where
δ
(
W
)
is the set of edges with only one endnode in
W
. This article proposes several distinct results about the weakly connected independent sets of a graph obtained by corona or join operations: the complete description of the wcis polytope for a corona or a join of two graphs of which we know the wcis polytopes or the maximal independent set polytopes, and the consequences of these graph operations on the minimum weight weakly connected independent set problem (MWWCISP). A class of graphs is also inductively defined from the connected bipartite graphs, the cycles and the strongly chordal graphs, for which the MWWCISP is polynomially solvable. This work is a direct continuation of the article (Bendali et al. in Discrete Optim 22:87–110,
2016
) where a similar theorem about complete description of the wcis polytope has been given for 1-sum operation.</description><identifier>ISSN: 1382-6905</identifier><identifier>EISSN: 1573-2886</identifier><identifier>DOI: 10.1007/s10878-018-0275-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Combinatorics ; Computer Science ; Convex and Discrete Geometry ; Discrete Mathematics ; Graphs ; Mathematical Modeling and Industrial Mathematics ; Mathematics ; Mathematics and Statistics ; Minimum weight ; Operations Research ; Operations Research/Decision Theory ; Optimization ; Polytopes ; Theory of Computation</subject><ispartof>Journal of combinatorial optimization, 2018-10, Vol.36 (3), p.1007-1023</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>Copyright Springer Science & Business Media 2018</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c302t-9b826c94939430cf9a92b13e925e75f07ffed5ff2b5226757e69ee3b8a335edb3</cites><orcidid>0000-0002-6147-5101 ; 0009-0000-1137-935X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10878-018-0275-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10878-018-0275-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>230,314,780,784,885,27924,27925,41488,42557,51319</link.rule.ids><backlink>$$Uhttps://uca.hal.science/hal-02042592$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Bendali, F.</creatorcontrib><creatorcontrib>Mailfert, J.</creatorcontrib><title>The weakly connected independent set polytope in corona and join of graphs</title><title>Journal of combinatorial optimization</title><addtitle>J Comb Optim</addtitle><description>Given a connected undirected graph
G
=
(
V
,
E
)
, a subset
W
of nodes of
G
is a weakly connected independent set if
W
is an independent set and the partial graph
(
V
,
δ
(
W
)
)
is connected, where
δ
(
W
)
is the set of edges with only one endnode in
W
. This article proposes several distinct results about the weakly connected independent sets of a graph obtained by corona or join operations: the complete description of the wcis polytope for a corona or a join of two graphs of which we know the wcis polytopes or the maximal independent set polytopes, and the consequences of these graph operations on the minimum weight weakly connected independent set problem (MWWCISP). A class of graphs is also inductively defined from the connected bipartite graphs, the cycles and the strongly chordal graphs, for which the MWWCISP is polynomially solvable. This work is a direct continuation of the article (Bendali et al. in Discrete Optim 22:87–110,
2016
) where a similar theorem about complete description of the wcis polytope has been given for 1-sum operation.</description><subject>Combinatorics</subject><subject>Computer Science</subject><subject>Convex and Discrete Geometry</subject><subject>Discrete Mathematics</subject><subject>Graphs</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Minimum weight</subject><subject>Operations Research</subject><subject>Operations Research/Decision Theory</subject><subject>Optimization</subject><subject>Polytopes</subject><subject>Theory of Computation</subject><issn>1382-6905</issn><issn>1573-2886</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kE1PxCAQhonRxPXjB3hr4slDdYBSynGzUVeziZf1TGg77IcVKnQ1--9lU6MnDwwzw_O-IS8hVxRuKYC8ixQqWeVA02FS5OqITKiQPGdVVR6nnlcsLxWIU3IW4xYAUl9MyPNyjdkXmrdunzXeOWwGbLONa7HHVNyQRRyy3nf7wfeYHhIVvDOZcW229Wn2NlsF06_jBTmxpot4-XOfk9eH--Vsni9eHp9m00XecGBDruqKlY0qFFcFh8Yqo1hNOSomUAoL0lpshbWsFoyVUkgsFSKvK8O5wLbm5-Rm9F2bTvdh827CXnuz0fPpQh92wKBgQrFPmtjrke2D_9hhHPTW74JL39MMlAJJSygTRUeqCT7GgPbXloI-xKvHeHWKVx_i1Spp2KiJiXUrDH_O_4u-ATyye98</recordid><startdate>20181001</startdate><enddate>20181001</enddate><creator>Bendali, F.</creator><creator>Mailfert, J.</creator><general>Springer US</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-6147-5101</orcidid><orcidid>https://orcid.org/0009-0000-1137-935X</orcidid></search><sort><creationdate>20181001</creationdate><title>The weakly connected independent set polytope in corona and join of graphs</title><author>Bendali, F. ; Mailfert, J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c302t-9b826c94939430cf9a92b13e925e75f07ffed5ff2b5226757e69ee3b8a335edb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Combinatorics</topic><topic>Computer Science</topic><topic>Convex and Discrete Geometry</topic><topic>Discrete Mathematics</topic><topic>Graphs</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Minimum weight</topic><topic>Operations Research</topic><topic>Operations Research/Decision Theory</topic><topic>Optimization</topic><topic>Polytopes</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bendali, F.</creatorcontrib><creatorcontrib>Mailfert, J.</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Journal of combinatorial optimization</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bendali, F.</au><au>Mailfert, J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The weakly connected independent set polytope in corona and join of graphs</atitle><jtitle>Journal of combinatorial optimization</jtitle><stitle>J Comb Optim</stitle><date>2018-10-01</date><risdate>2018</risdate><volume>36</volume><issue>3</issue><spage>1007</spage><epage>1023</epage><pages>1007-1023</pages><issn>1382-6905</issn><eissn>1573-2886</eissn><abstract>Given a connected undirected graph
G
=
(
V
,
E
)
, a subset
W
of nodes of
G
is a weakly connected independent set if
W
is an independent set and the partial graph
(
V
,
δ
(
W
)
)
is connected, where
δ
(
W
)
is the set of edges with only one endnode in
W
. This article proposes several distinct results about the weakly connected independent sets of a graph obtained by corona or join operations: the complete description of the wcis polytope for a corona or a join of two graphs of which we know the wcis polytopes or the maximal independent set polytopes, and the consequences of these graph operations on the minimum weight weakly connected independent set problem (MWWCISP). A class of graphs is also inductively defined from the connected bipartite graphs, the cycles and the strongly chordal graphs, for which the MWWCISP is polynomially solvable. This work is a direct continuation of the article (Bendali et al. in Discrete Optim 22:87–110,
2016
) where a similar theorem about complete description of the wcis polytope has been given for 1-sum operation.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10878-018-0275-9</doi><tpages>17</tpages><orcidid>https://orcid.org/0000-0002-6147-5101</orcidid><orcidid>https://orcid.org/0009-0000-1137-935X</orcidid></addata></record> |
| fulltext | fulltext |
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| ispartof | Journal of combinatorial optimization, 2018-10, Vol.36 (3), p.1007-1023 |
| issn | 1382-6905 1573-2886 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_02042592v1 |
| source | SpringerLink Journals |
| subjects | Combinatorics Computer Science Convex and Discrete Geometry Discrete Mathematics Graphs Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Minimum weight Operations Research Operations Research/Decision Theory Optimization Polytopes Theory of Computation |
| title | The weakly connected independent set polytope in corona and join of graphs |
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