Edge-Disjoint Steiner Trees and Connectors in Graphs
Kriesell (J Comb Theory Ser B 88:53–65, 2003) proposed Conjecture 1: If S ⊆ V ( G ) is 2 k -edge-connected in a graph G , then G contains k edge-disjoint S -Steiner trees. West and Wu (J Comb Theory Ser B 102:186–205, 1961) posed Conjecture 2: If S ⊆ V ( G ) is 3 k -edge-connected in a graph G , t...
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| Veröffentlicht in: | Graphs and combinatorics 2023-04, Vol.39 (2), Article 23 |
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| creator | Li, Hengzhe Liu, Huayue Liu, Jianbing Mao, Yaping |
| description | Kriesell (J Comb Theory Ser B 88:53–65, 2003) proposed Conjecture 1: If
S
⊆
V
(
G
)
is 2
k
-edge-connected in a graph
G
, then
G
contains
k
edge-disjoint
S
-Steiner trees. West and Wu (J Comb Theory Ser B 102:186–205, 1961) posed Conjecture 2: If
S
⊆
V
(
G
)
is 3
k
-edge-connected in a graph
G
, then
G
contains
k
edge-disjoint
S
-connectors, which is an analogue for
S
-connectors of Kriesell’s Conjecture. This paper shows If
|
V
(
G
)
-
S
|
≤
k
,
then Conjecture 1 is true and if
|
V
(
G
)
-
S
|
≤
2
k
,
then Conjecture 2 is true. This paper also investigate the validity of two conjectures with certain additional conditions of
|
V
(
G
)
-
S
|
or |
S
|. |
| doi_str_mv | 10.1007/s00373-023-02621-3 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2777432132</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2777432132</sourcerecordid><originalsourceid>FETCH-LOGICAL-c200t-86254ca64e81b6003c0b9ab79f0129bad9eca736174254e2621b5e333102e1023</originalsourceid><addsrcrecordid>eNp9kM1OwzAQhC0EEuXnBThF4mzY9TpxfUSlFKRKHChny0m3JRU4xU4PvD0OQeLGYbSXb2ZHI8QVwg0CmNsEQIYkqEGVQklHYoKaSlla1MdiAhZRAqI9FWcp7QCgRA0ToefrLcv7Nu26NvTFS89t4FisInMqfFgXsy4EbvoupqINxSL6_Vu6ECcb_5748veei9eH-Wr2KJfPi6fZ3VI2CqCX00qVuvGV5inWVW7YQG19bewGUNnary033lCFRmeQh951yUSEoDiLzsX1mLuP3eeBU-923SGG_NIpY4wmhTRQaqSa2KUUeeP2sf3w8cshuGEdN67jcqL7WcdRNtFoShkOW45_0f-4vgFHMGSJ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2777432132</pqid></control><display><type>article</type><title>Edge-Disjoint Steiner Trees and Connectors in Graphs</title><source>SpringerLink Journals - AutoHoldings</source><creator>Li, Hengzhe ; Liu, Huayue ; Liu, Jianbing ; Mao, Yaping</creator><creatorcontrib>Li, Hengzhe ; Liu, Huayue ; Liu, Jianbing ; Mao, Yaping</creatorcontrib><description>Kriesell (J Comb Theory Ser B 88:53–65, 2003) proposed Conjecture 1: If
S
⊆
V
(
G
)
is 2
k
-edge-connected in a graph
G
, then
G
contains
k
edge-disjoint
S
-Steiner trees. West and Wu (J Comb Theory Ser B 102:186–205, 1961) posed Conjecture 2: If
S
⊆
V
(
G
)
is 3
k
-edge-connected in a graph
G
, then
G
contains
k
edge-disjoint
S
-connectors, which is an analogue for
S
-connectors of Kriesell’s Conjecture. This paper shows If
|
V
(
G
)
-
S
|
≤
k
,
then Conjecture 1 is true and if
|
V
(
G
)
-
S
|
≤
2
k
,
then Conjecture 2 is true. This paper also investigate the validity of two conjectures with certain additional conditions of
|
V
(
G
)
-
S
|
or |
S
|.</description><identifier>ISSN: 0911-0119</identifier><identifier>EISSN: 1435-5914</identifier><identifier>DOI: 10.1007/s00373-023-02621-3</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Combinatorics ; Connectors ; Engineering Design ; Mathematics ; Mathematics and Statistics ; Original Paper</subject><ispartof>Graphs and combinatorics, 2023-04, Vol.39 (2), Article 23</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Japan KK, part of Springer Nature 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><cites>FETCH-LOGICAL-c200t-86254ca64e81b6003c0b9ab79f0129bad9eca736174254e2621b5e333102e1023</cites><orcidid>0000-0001-6004-971X</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/s00373-023-02621-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00373-023-02621-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Li, Hengzhe</creatorcontrib><creatorcontrib>Liu, Huayue</creatorcontrib><creatorcontrib>Liu, Jianbing</creatorcontrib><creatorcontrib>Mao, Yaping</creatorcontrib><title>Edge-Disjoint Steiner Trees and Connectors in Graphs</title><title>Graphs and combinatorics</title><addtitle>Graphs and Combinatorics</addtitle><description>Kriesell (J Comb Theory Ser B 88:53–65, 2003) proposed Conjecture 1: If
S
⊆
V
(
G
)
is 2
k
-edge-connected in a graph
G
, then
G
contains
k
edge-disjoint
S
-Steiner trees. West and Wu (J Comb Theory Ser B 102:186–205, 1961) posed Conjecture 2: If
S
⊆
V
(
G
)
is 3
k
-edge-connected in a graph
G
, then
G
contains
k
edge-disjoint
S
-connectors, which is an analogue for
S
-connectors of Kriesell’s Conjecture. This paper shows If
|
V
(
G
)
-
S
|
≤
k
,
then Conjecture 1 is true and if
|
V
(
G
)
-
S
|
≤
2
k
,
then Conjecture 2 is true. This paper also investigate the validity of two conjectures with certain additional conditions of
|
V
(
G
)
-
S
|
or |
S
|.</description><subject>Combinatorics</subject><subject>Connectors</subject><subject>Engineering Design</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><issn>0911-0119</issn><issn>1435-5914</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kM1OwzAQhC0EEuXnBThF4mzY9TpxfUSlFKRKHChny0m3JRU4xU4PvD0OQeLGYbSXb2ZHI8QVwg0CmNsEQIYkqEGVQklHYoKaSlla1MdiAhZRAqI9FWcp7QCgRA0ToefrLcv7Nu26NvTFS89t4FisInMqfFgXsy4EbvoupqINxSL6_Vu6ECcb_5748veei9eH-Wr2KJfPi6fZ3VI2CqCX00qVuvGV5inWVW7YQG19bewGUNnary033lCFRmeQh951yUSEoDiLzsX1mLuP3eeBU-923SGG_NIpY4wmhTRQaqSa2KUUeeP2sf3w8cshuGEdN67jcqL7WcdRNtFoShkOW45_0f-4vgFHMGSJ</recordid><startdate>20230401</startdate><enddate>20230401</enddate><creator>Li, Hengzhe</creator><creator>Liu, Huayue</creator><creator>Liu, Jianbing</creator><creator>Mao, Yaping</creator><general>Springer Japan</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-6004-971X</orcidid></search><sort><creationdate>20230401</creationdate><title>Edge-Disjoint Steiner Trees and Connectors in Graphs</title><author>Li, Hengzhe ; Liu, Huayue ; Liu, Jianbing ; Mao, Yaping</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-86254ca64e81b6003c0b9ab79f0129bad9eca736174254e2621b5e333102e1023</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Combinatorics</topic><topic>Connectors</topic><topic>Engineering Design</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Hengzhe</creatorcontrib><creatorcontrib>Liu, Huayue</creatorcontrib><creatorcontrib>Liu, Jianbing</creatorcontrib><creatorcontrib>Mao, Yaping</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</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>Graphs and combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Hengzhe</au><au>Liu, Huayue</au><au>Liu, Jianbing</au><au>Mao, Yaping</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Edge-Disjoint Steiner Trees and Connectors in Graphs</atitle><jtitle>Graphs and combinatorics</jtitle><stitle>Graphs and Combinatorics</stitle><date>2023-04-01</date><risdate>2023</risdate><volume>39</volume><issue>2</issue><artnum>23</artnum><issn>0911-0119</issn><eissn>1435-5914</eissn><abstract>Kriesell (J Comb Theory Ser B 88:53–65, 2003) proposed Conjecture 1: If
S
⊆
V
(
G
)
is 2
k
-edge-connected in a graph
G
, then
G
contains
k
edge-disjoint
S
-Steiner trees. West and Wu (J Comb Theory Ser B 102:186–205, 1961) posed Conjecture 2: If
S
⊆
V
(
G
)
is 3
k
-edge-connected in a graph
G
, then
G
contains
k
edge-disjoint
S
-connectors, which is an analogue for
S
-connectors of Kriesell’s Conjecture. This paper shows If
|
V
(
G
)
-
S
|
≤
k
,
then Conjecture 1 is true and if
|
V
(
G
)
-
S
|
≤
2
k
,
then Conjecture 2 is true. This paper also investigate the validity of two conjectures with certain additional conditions of
|
V
(
G
)
-
S
|
or |
S
|.</abstract><cop>Tokyo</cop><pub>Springer Japan</pub><doi>10.1007/s00373-023-02621-3</doi><orcidid>https://orcid.org/0000-0001-6004-971X</orcidid></addata></record> |
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| ispartof | Graphs and combinatorics, 2023-04, Vol.39 (2), Article 23 |
| issn | 0911-0119 1435-5914 |
| language | eng |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Combinatorics Connectors Engineering Design Mathematics Mathematics and Statistics Original Paper |
| title | Edge-Disjoint Steiner Trees and Connectors in Graphs |
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