Five‐cycle double cover and shortest cycle cover
The 5‐even subgraph cycle double cover conjecture (5‐CDC conjecture) asserts that every bridgeless graph has a 5‐even subgraph double cover. A shortest even subgraph cover of a graph G is a family of even subgraphs which cover all the edges of G and the sum of their lengths is minimum. It is conject...
Gespeichert in:
| Veröffentlicht in: | Journal of graph theory 2025-01, Vol.108 (1), p.39-49 |
|---|---|
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 49 |
|---|---|
| container_issue | 1 |
| container_start_page | 39 |
| container_title | Journal of graph theory |
| container_volume | 108 |
| creator | Liu, Siyan Hao, Rong‐Xia Luo, Rong Zhang, Cun‐Quan |
| description | The 5‐even subgraph cycle double cover conjecture (5‐CDC conjecture) asserts that every bridgeless graph has a 5‐even subgraph double cover. A shortest even subgraph cover of a graph
G is a family of even subgraphs which cover all the edges of
G and the sum of their lengths is minimum. It is conjectured that every bridgeless graph
G has an even subgraph cover with total length at most
21
15
∣
E
(
G
)
∣. In this paper, we study those two conjectures for weak oddness 2 cubic graphs and present a sufficient condition for such graphs to have a 5‐CDC containing a member with many vertices. As a corollary, we show that for every oddness 2 cubic graph
G satisfying the sufficient condition has a 4‐even subgraph
(
1
,
2
)‐cover with total length at most
20
15
∣
E
(
G
)
∣
+
2. We also show that every oddness 2 cubic graph
G with girth at least 30 has a 5‐CDC containing a member of length at least
9
10
∣
V
(
G
)
∣ and thus it has a 4‐even subgraph
(
1
,
2
)‐cover with total length at most
21
15
∣
E
(
G
)
∣. |
| doi_str_mv | 10.1002/jgt.23164 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_3128851745</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>3128851745</sourcerecordid><originalsourceid>FETCH-LOGICAL-c2574-5a22d401d3e3c13f29c59448c596d67a56244149fa13feb5798bfd9fa7465f0b3</originalsourceid><addsrcrecordid>eNp1kEtOwzAQhi0EEqGw4AaRWLFI68fYiZeoogVUiU1ZW47jQKJQF7spyo4j9IycBNOwZTOjmf-bh36ErgmeEozprH3dTSkjAk5QQrDMM0xIcYoSzARkElM4RxchtDi2OS4SRBfN3n5_HcxgOptWri9jMm5vfao3VRrenN_ZsEtH_ShcorNad8Fe_eUJelncr-cP2ep5-Ti_W2WG8hwyrimtAJOKWWYIq6k0XAIUMYpK5JoLCkBA1jqKtuS5LMq6imUOgte4ZBN0M-7devfRxydU63q_iScVI7QoOMmBR-p2pIx3IXhbq61v3rUfFMHq1xIVLVFHSyI7G9nPprPD_6B6Wq7HiR9uRWGs</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>3128851745</pqid></control><display><type>article</type><title>Five‐cycle double cover and shortest cycle cover</title><source>Wiley Online Library Journals Frontfile Complete</source><creator>Liu, Siyan ; Hao, Rong‐Xia ; Luo, Rong ; Zhang, Cun‐Quan</creator><creatorcontrib>Liu, Siyan ; Hao, Rong‐Xia ; Luo, Rong ; Zhang, Cun‐Quan</creatorcontrib><description>The 5‐even subgraph cycle double cover conjecture (5‐CDC conjecture) asserts that every bridgeless graph has a 5‐even subgraph double cover. A shortest even subgraph cover of a graph
G is a family of even subgraphs which cover all the edges of
G and the sum of their lengths is minimum. It is conjectured that every bridgeless graph
G has an even subgraph cover with total length at most
21
15
∣
E
(
G
)
∣. In this paper, we study those two conjectures for weak oddness 2 cubic graphs and present a sufficient condition for such graphs to have a 5‐CDC containing a member with many vertices. As a corollary, we show that for every oddness 2 cubic graph
G satisfying the sufficient condition has a 4‐even subgraph
(
1
,
2
)‐cover with total length at most
20
15
∣
E
(
G
)
∣
+
2. We also show that every oddness 2 cubic graph
G with girth at least 30 has a 5‐CDC containing a member of length at least
9
10
∣
V
(
G
)
∣ and thus it has a 4‐even subgraph
(
1
,
2
)‐cover with total length at most
21
15
∣
E
(
G
)
∣.</description><identifier>ISSN: 0364-9024</identifier><identifier>EISSN: 1097-0118</identifier><identifier>DOI: 10.1002/jgt.23164</identifier><language>eng</language><publisher>Hoboken: Wiley Subscription Services, Inc</publisher><subject>4‐even subgraph cover ; 4‐flow ; Apexes ; Graph theory ; Graphs ; oddness ; shortest even subgraph cover</subject><ispartof>Journal of graph theory, 2025-01, Vol.108 (1), p.39-49</ispartof><rights>2024 Wiley Periodicals LLC.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2574-5a22d401d3e3c13f29c59448c596d67a56244149fa13feb5798bfd9fa7465f0b3</cites><orcidid>0000-0001-6265-0429 ; 0000-0001-5583-4481</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fjgt.23164$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fjgt.23164$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids></links><search><creatorcontrib>Liu, Siyan</creatorcontrib><creatorcontrib>Hao, Rong‐Xia</creatorcontrib><creatorcontrib>Luo, Rong</creatorcontrib><creatorcontrib>Zhang, Cun‐Quan</creatorcontrib><title>Five‐cycle double cover and shortest cycle cover</title><title>Journal of graph theory</title><description>The 5‐even subgraph cycle double cover conjecture (5‐CDC conjecture) asserts that every bridgeless graph has a 5‐even subgraph double cover. A shortest even subgraph cover of a graph
G is a family of even subgraphs which cover all the edges of
G and the sum of their lengths is minimum. It is conjectured that every bridgeless graph
G has an even subgraph cover with total length at most
21
15
∣
E
(
G
)
∣. In this paper, we study those two conjectures for weak oddness 2 cubic graphs and present a sufficient condition for such graphs to have a 5‐CDC containing a member with many vertices. As a corollary, we show that for every oddness 2 cubic graph
G satisfying the sufficient condition has a 4‐even subgraph
(
1
,
2
)‐cover with total length at most
20
15
∣
E
(
G
)
∣
+
2. We also show that every oddness 2 cubic graph
G with girth at least 30 has a 5‐CDC containing a member of length at least
9
10
∣
V
(
G
)
∣ and thus it has a 4‐even subgraph
(
1
,
2
)‐cover with total length at most
21
15
∣
E
(
G
)
∣.</description><subject>4‐even subgraph cover</subject><subject>4‐flow</subject><subject>Apexes</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>oddness</subject><subject>shortest even subgraph cover</subject><issn>0364-9024</issn><issn>1097-0118</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2025</creationdate><recordtype>article</recordtype><recordid>eNp1kEtOwzAQhi0EEqGw4AaRWLFI68fYiZeoogVUiU1ZW47jQKJQF7spyo4j9IycBNOwZTOjmf-bh36ErgmeEozprH3dTSkjAk5QQrDMM0xIcYoSzARkElM4RxchtDi2OS4SRBfN3n5_HcxgOptWri9jMm5vfao3VRrenN_ZsEtH_ShcorNad8Fe_eUJelncr-cP2ep5-Ti_W2WG8hwyrimtAJOKWWYIq6k0XAIUMYpK5JoLCkBA1jqKtuS5LMq6imUOgte4ZBN0M-7devfRxydU63q_iScVI7QoOMmBR-p2pIx3IXhbq61v3rUfFMHq1xIVLVFHSyI7G9nPprPD_6B6Wq7HiR9uRWGs</recordid><startdate>202501</startdate><enddate>202501</enddate><creator>Liu, Siyan</creator><creator>Hao, Rong‐Xia</creator><creator>Luo, Rong</creator><creator>Zhang, Cun‐Quan</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-6265-0429</orcidid><orcidid>https://orcid.org/0000-0001-5583-4481</orcidid></search><sort><creationdate>202501</creationdate><title>Five‐cycle double cover and shortest cycle cover</title><author>Liu, Siyan ; Hao, Rong‐Xia ; Luo, Rong ; Zhang, Cun‐Quan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2574-5a22d401d3e3c13f29c59448c596d67a56244149fa13feb5798bfd9fa7465f0b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2025</creationdate><topic>4‐even subgraph cover</topic><topic>4‐flow</topic><topic>Apexes</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>oddness</topic><topic>shortest even subgraph cover</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Liu, Siyan</creatorcontrib><creatorcontrib>Hao, Rong‐Xia</creatorcontrib><creatorcontrib>Luo, Rong</creatorcontrib><creatorcontrib>Zhang, Cun‐Quan</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of graph theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Liu, Siyan</au><au>Hao, Rong‐Xia</au><au>Luo, Rong</au><au>Zhang, Cun‐Quan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Five‐cycle double cover and shortest cycle cover</atitle><jtitle>Journal of graph theory</jtitle><date>2025-01</date><risdate>2025</risdate><volume>108</volume><issue>1</issue><spage>39</spage><epage>49</epage><pages>39-49</pages><issn>0364-9024</issn><eissn>1097-0118</eissn><abstract>The 5‐even subgraph cycle double cover conjecture (5‐CDC conjecture) asserts that every bridgeless graph has a 5‐even subgraph double cover. A shortest even subgraph cover of a graph
G is a family of even subgraphs which cover all the edges of
G and the sum of their lengths is minimum. It is conjectured that every bridgeless graph
G has an even subgraph cover with total length at most
21
15
∣
E
(
G
)
∣. In this paper, we study those two conjectures for weak oddness 2 cubic graphs and present a sufficient condition for such graphs to have a 5‐CDC containing a member with many vertices. As a corollary, we show that for every oddness 2 cubic graph
G satisfying the sufficient condition has a 4‐even subgraph
(
1
,
2
)‐cover with total length at most
20
15
∣
E
(
G
)
∣
+
2. We also show that every oddness 2 cubic graph
G with girth at least 30 has a 5‐CDC containing a member of length at least
9
10
∣
V
(
G
)
∣ and thus it has a 4‐even subgraph
(
1
,
2
)‐cover with total length at most
21
15
∣
E
(
G
)
∣.</abstract><cop>Hoboken</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/jgt.23164</doi><tpages>11</tpages><orcidid>https://orcid.org/0000-0001-6265-0429</orcidid><orcidid>https://orcid.org/0000-0001-5583-4481</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0364-9024 |
| ispartof | Journal of graph theory, 2025-01, Vol.108 (1), p.39-49 |
| issn | 0364-9024 1097-0118 |
| language | eng |
| recordid | cdi_proquest_journals_3128851745 |
| source | Wiley Online Library Journals Frontfile Complete |
| subjects | 4‐even subgraph cover 4‐flow Apexes Graph theory Graphs oddness shortest even subgraph cover |
| title | Five‐cycle double cover and shortest cycle cover |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-19T09%3A49%3A21IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Five%E2%80%90cycle%20double%20cover%20and%20shortest%20cycle%20cover&rft.jtitle=Journal%20of%20graph%20theory&rft.au=Liu,%20Siyan&rft.date=2025-01&rft.volume=108&rft.issue=1&rft.spage=39&rft.epage=49&rft.pages=39-49&rft.issn=0364-9024&rft.eissn=1097-0118&rft_id=info:doi/10.1002/jgt.23164&rft_dat=%3Cproquest_cross%3E3128851745%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=3128851745&rft_id=info:pmid/&rfr_iscdi=true |