On the Linear Arboricity of Graphs with Treewidth at Most Four
The linear arboricity la ( G ) of a graph G is the minimum number of linear forests that partition the edges of G . Akiyama, Exoo and Harary conjectured that ⌈ Δ 2 ⌉ ≤ l a ( G ) ≤ ⌈ Δ + 1 2 ⌉ for any graph G with maximum degree Δ , and proved the conjecture holds for forests. This conjecture has bee...
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| Veröffentlicht in: | Graphs and combinatorics 2023-08, Vol.39 (4), Article 70 |
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| creator | Chen, Hong-Yu Lai, Hong-Jian |
| description | The linear arboricity
la
(
G
) of a graph
G
is the minimum number of linear forests that partition the edges of
G
. Akiyama, Exoo and Harary conjectured that
⌈
Δ
2
⌉
≤
l
a
(
G
)
≤
⌈
Δ
+
1
2
⌉
for any graph
G
with maximum degree
Δ
, and proved the conjecture holds for forests. This conjecture has been verified for certain graph families with treewidth at most 3. In the paper we improve these former results by validating the conjecture for all graphs with treewidth at most 4. |
| doi_str_mv | 10.1007/s00373-023-02673-5 |
| format | Article |
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la
(
G
) of a graph
G
is the minimum number of linear forests that partition the edges of
G
. Akiyama, Exoo and Harary conjectured that
⌈
Δ
2
⌉
≤
l
a
(
G
)
≤
⌈
Δ
+
1
2
⌉
for any graph
G
with maximum degree
Δ
, and proved the conjecture holds for forests. This conjecture has been verified for certain graph families with treewidth at most 3. In the paper we improve these former results by validating the conjecture for all graphs with treewidth at most 4.</description><identifier>ISSN: 0911-0119</identifier><identifier>EISSN: 1435-5914</identifier><identifier>DOI: 10.1007/s00373-023-02673-5</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Combinatorics ; Engineering Design ; Graphs ; Mathematics ; Mathematics and Statistics ; Original Paper</subject><ispartof>Graphs and combinatorics, 2023-08, Vol.39 (4), Article 70</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-c270t-90645e48b1fb348317a04801982978271575c17655172ef2b191716ab230ebd63</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00373-023-02673-5$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00373-023-02673-5$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Chen, Hong-Yu</creatorcontrib><creatorcontrib>Lai, Hong-Jian</creatorcontrib><title>On the Linear Arboricity of Graphs with Treewidth at Most Four</title><title>Graphs and combinatorics</title><addtitle>Graphs and Combinatorics</addtitle><description>The linear arboricity
la
(
G
) of a graph
G
is the minimum number of linear forests that partition the edges of
G
. Akiyama, Exoo and Harary conjectured that
⌈
Δ
2
⌉
≤
l
a
(
G
)
≤
⌈
Δ
+
1
2
⌉
for any graph
G
with maximum degree
Δ
, and proved the conjecture holds for forests. This conjecture has been verified for certain graph families with treewidth at most 3. In the paper we improve these former results by validating the conjecture for all graphs with treewidth at most 4.</description><subject>Combinatorics</subject><subject>Engineering Design</subject><subject>Graphs</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>eNp9kE1LAzEQhoMouFb_gKeA59WZfGw2F6EUW4VKL_Ucstus3aK7a5JS-u9NXcGbh2Hm8H4wDyG3CPcIoB4CAFc8B3aaIl3yjGQouMylRnFOMtCIOSDqS3IVwg4AJArIyOOqo3Hr6LLtnPV06qvet3Ubj7Rv6MLbYRvooY1buvbOHdpNumykr32IdN7v_TW5aOxHcDe_e0Le5k_r2XO-XC1eZtNlXjMFMddQCOlEWWFTcVFyVBZECahLplXJFEola1SFlKiYa1iFGhUWtmIcXLUp-ITcjbmD77_2LkSzS-1dqjQs-VX6RUJSsVFV-z4E7xoz-PbT-qNBMCdOZuRkEifzw8nIZOKjKSRx9-78X_Q_rm9BUWdD</recordid><startdate>20230801</startdate><enddate>20230801</enddate><creator>Chen, Hong-Yu</creator><creator>Lai, Hong-Jian</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></search><sort><creationdate>20230801</creationdate><title>On the Linear Arboricity of Graphs with Treewidth at Most Four</title><author>Chen, Hong-Yu ; Lai, Hong-Jian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c270t-90645e48b1fb348317a04801982978271575c17655172ef2b191716ab230ebd63</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Combinatorics</topic><topic>Engineering Design</topic><topic>Graphs</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chen, Hong-Yu</creatorcontrib><creatorcontrib>Lai, Hong-Jian</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>Chen, Hong-Yu</au><au>Lai, Hong-Jian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the Linear Arboricity of Graphs with Treewidth at Most Four</atitle><jtitle>Graphs and combinatorics</jtitle><stitle>Graphs and Combinatorics</stitle><date>2023-08-01</date><risdate>2023</risdate><volume>39</volume><issue>4</issue><artnum>70</artnum><issn>0911-0119</issn><eissn>1435-5914</eissn><abstract>The linear arboricity
la
(
G
) of a graph
G
is the minimum number of linear forests that partition the edges of
G
. Akiyama, Exoo and Harary conjectured that
⌈
Δ
2
⌉
≤
l
a
(
G
)
≤
⌈
Δ
+
1
2
⌉
for any graph
G
with maximum degree
Δ
, and proved the conjecture holds for forests. This conjecture has been verified for certain graph families with treewidth at most 3. In the paper we improve these former results by validating the conjecture for all graphs with treewidth at most 4.</abstract><cop>Tokyo</cop><pub>Springer Japan</pub><doi>10.1007/s00373-023-02673-5</doi></addata></record> |
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| ispartof | Graphs and combinatorics, 2023-08, Vol.39 (4), Article 70 |
| issn | 0911-0119 1435-5914 |
| language | eng |
| recordid | cdi_proquest_journals_2827714050 |
| source | SpringerNature Journals |
| subjects | Combinatorics Engineering Design Graphs Mathematics Mathematics and Statistics Original Paper |
| title | On the Linear Arboricity of Graphs with Treewidth at Most Four |
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