Graphs with Gp-connected medians
The median of a graph G with weighted vertices is the set of all vertices x minimizing the sum of weighted distances from x to the vertices of G . For any integer p ≥ 2 , we characterize the graphs in which, with respect to any non-negative weights, median sets always induce connected subgraphs in t...
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| Veröffentlicht in: | Mathematical programming 2024, Vol.203 (1-2), p.369-420 |
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| creator | Bénéteau, Laurine Chalopin, Jérémie Chepoi, Victor Vaxès, Yann |
| description | The median of a graph
G
with weighted vertices is the set of all vertices
x
minimizing the sum of weighted distances from
x
to the vertices of
G
. For any integer
p
≥
2
, we characterize the graphs in which, with respect to any non-negative weights, median sets always induce connected subgraphs in the
p
th power
G
p
of
G
. This extends some characterizations of graphs with connected medians (case
p
=
1
) provided by Bandelt and Chepoi (SIAM J Discrete Math 15(2):268–282, 2002.
https://doi.org/10.1137/S089548019936360X
). The characteristic conditions can be tested in polynomial time for any
p
. We also show that several important classes of graphs in metric graph theory, including bridged graphs (and thus chordal graphs), graphs with convex balls, bucolic graphs, and bipartite absolute retracts, have
G
2
-connected medians. Extending the result of Bandelt and Chepoi that basis graphs of matroids are graphs with connected medians, we characterize the isometric subgraphs of Johnson graphs and of halved-cubes with connected medians. |
| doi_str_mv | 10.1007/s10107-023-01939-3 |
| format | Article |
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G
with weighted vertices is the set of all vertices
x
minimizing the sum of weighted distances from
x
to the vertices of
G
. For any integer
p
≥
2
, we characterize the graphs in which, with respect to any non-negative weights, median sets always induce connected subgraphs in the
p
th power
G
p
of
G
. This extends some characterizations of graphs with connected medians (case
p
=
1
) provided by Bandelt and Chepoi (SIAM J Discrete Math 15(2):268–282, 2002.
https://doi.org/10.1137/S089548019936360X
). The characteristic conditions can be tested in polynomial time for any
p
. We also show that several important classes of graphs in metric graph theory, including bridged graphs (and thus chordal graphs), graphs with convex balls, bucolic graphs, and bipartite absolute retracts, have
G
2
-connected medians. Extending the result of Bandelt and Chepoi that basis graphs of matroids are graphs with connected medians, we characterize the isometric subgraphs of Johnson graphs and of halved-cubes with connected medians.</description><identifier>ISSN: 0025-5610</identifier><identifier>EISSN: 1436-4646</identifier><identifier>DOI: 10.1007/s10107-023-01939-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Apexes ; Calculus of Variations and Optimal Control; Optimization ; Combinatorics ; Cubes ; Full Length Paper ; Graph theory ; Graphs ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Numerical Analysis ; Polynomials ; Theoretical</subject><ispartof>Mathematical programming, 2024, Vol.203 (1-2), p.369-420</ispartof><rights>Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0000-0002-0481-7312</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/s10107-023-01939-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10107-023-01939-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Bénéteau, Laurine</creatorcontrib><creatorcontrib>Chalopin, Jérémie</creatorcontrib><creatorcontrib>Chepoi, Victor</creatorcontrib><creatorcontrib>Vaxès, Yann</creatorcontrib><title>Graphs with Gp-connected medians</title><title>Mathematical programming</title><addtitle>Math. Program</addtitle><description>The median of a graph
G
with weighted vertices is the set of all vertices
x
minimizing the sum of weighted distances from
x
to the vertices of
G
. For any integer
p
≥
2
, we characterize the graphs in which, with respect to any non-negative weights, median sets always induce connected subgraphs in the
p
th power
G
p
of
G
. This extends some characterizations of graphs with connected medians (case
p
=
1
) provided by Bandelt and Chepoi (SIAM J Discrete Math 15(2):268–282, 2002.
https://doi.org/10.1137/S089548019936360X
). The characteristic conditions can be tested in polynomial time for any
p
. We also show that several important classes of graphs in metric graph theory, including bridged graphs (and thus chordal graphs), graphs with convex balls, bucolic graphs, and bipartite absolute retracts, have
G
2
-connected medians. Extending the result of Bandelt and Chepoi that basis graphs of matroids are graphs with connected medians, we characterize the isometric subgraphs of Johnson graphs and of halved-cubes with connected medians.</description><subject>Apexes</subject><subject>Calculus of Variations and Optimal Control; Optimization</subject><subject>Combinatorics</subject><subject>Cubes</subject><subject>Full Length Paper</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Numerical Analysis</subject><subject>Polynomials</subject><subject>Theoretical</subject><issn>0025-5610</issn><issn>1436-4646</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNpFkE1LxDAURYMoWEf_gKuC6-h7eUmaLGXQjjDgZvah-ajTQdvadPDvWx1B7uJuDvfCYewW4R4BqoeMgFBxEMQBLVlOZ6xASZpLLfU5KwCE4kojXLKrnA8AgGRMwcp6asZ9Lr-6eV_WIw9D36cwp1h-pNg1fb5mF23zntPNX6_Y7vlpt97w7Wv9sn7c8hFVNXOLSVXSi9bI1nstglKGPKrYGG-lSUkGSVZqMkvQ-LbyQbfRL3CQMdKK3Z1mx2n4PKY8u8NwnPrl0QkrpLBgiBaKTlQep65_S9M_heB-TLiTCbeYcL8mHNE34wZPrQ</recordid><startdate>2024</startdate><enddate>2024</enddate><creator>Bénéteau, Laurine</creator><creator>Chalopin, Jérémie</creator><creator>Chepoi, Victor</creator><creator>Vaxès, Yann</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-0481-7312</orcidid></search><sort><creationdate>2024</creationdate><title>Graphs with Gp-connected medians</title><author>Bénéteau, Laurine ; Chalopin, Jérémie ; Chepoi, Victor ; Vaxès, Yann</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p157t-91e574b2f84fbb62c5583b15da8b948ee4c439463838318bf7bc6fdbfbbc4dd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Apexes</topic><topic>Calculus of Variations and Optimal Control; Optimization</topic><topic>Combinatorics</topic><topic>Cubes</topic><topic>Full Length Paper</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Numerical Analysis</topic><topic>Polynomials</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bénéteau, Laurine</creatorcontrib><creatorcontrib>Chalopin, Jérémie</creatorcontrib><creatorcontrib>Chepoi, Victor</creatorcontrib><creatorcontrib>Vaxès, Yann</creatorcontrib><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>Mathematical programming</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bénéteau, Laurine</au><au>Chalopin, Jérémie</au><au>Chepoi, Victor</au><au>Vaxès, Yann</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Graphs with Gp-connected medians</atitle><jtitle>Mathematical programming</jtitle><stitle>Math. Program</stitle><date>2024</date><risdate>2024</risdate><volume>203</volume><issue>1-2</issue><spage>369</spage><epage>420</epage><pages>369-420</pages><issn>0025-5610</issn><eissn>1436-4646</eissn><abstract>The median of a graph
G
with weighted vertices is the set of all vertices
x
minimizing the sum of weighted distances from
x
to the vertices of
G
. For any integer
p
≥
2
, we characterize the graphs in which, with respect to any non-negative weights, median sets always induce connected subgraphs in the
p
th power
G
p
of
G
. This extends some characterizations of graphs with connected medians (case
p
=
1
) provided by Bandelt and Chepoi (SIAM J Discrete Math 15(2):268–282, 2002.
https://doi.org/10.1137/S089548019936360X
). The characteristic conditions can be tested in polynomial time for any
p
. We also show that several important classes of graphs in metric graph theory, including bridged graphs (and thus chordal graphs), graphs with convex balls, bucolic graphs, and bipartite absolute retracts, have
G
2
-connected medians. Extending the result of Bandelt and Chepoi that basis graphs of matroids are graphs with connected medians, we characterize the isometric subgraphs of Johnson graphs and of halved-cubes with connected medians.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s10107-023-01939-3</doi><tpages>52</tpages><orcidid>https://orcid.org/0000-0002-0481-7312</orcidid></addata></record> |
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| subjects | Apexes Calculus of Variations and Optimal Control Optimization Combinatorics Cubes Full Length Paper Graph theory Graphs Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Polynomials Theoretical |
| title | Graphs with Gp-connected medians |
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