On Hamiltonicity of 3-Connected Claw-Free Graphs
Lai, Shao and Zhan (J Graph Theory 48:142–146, 2005 ) showed that every 3-connected N 2 -locally connected claw-free graph is Hamiltonian. In this paper, we generalize this result and show that every 3-connected claw-free graph G such that every locally disconnected vertex lies on some induced cycle...
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| Veröffentlicht in: | Graphs and combinatorics 2014-09, Vol.30 (5), p.1261-1269 |
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| container_title | Graphs and combinatorics |
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| creator | Tian, Runli Xiong, Liming Niu, Zhaohong |
| description | Lai, Shao and Zhan (J Graph Theory 48:142–146,
2005
) showed that every 3-connected
N
2
-locally connected claw-free graph is Hamiltonian. In this paper, we generalize this result and show that every 3-connected claw-free graph
G
such that every locally disconnected vertex lies on some induced cycle of length at least 4 with at most 4 edges contained in some triangle of
G
is Hamiltonian. It is best possible in some sense. |
| doi_str_mv | 10.1007/s00373-013-1343-7 |
| format | Article |
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2005
) showed that every 3-connected
N
2
-locally connected claw-free graph is Hamiltonian. In this paper, we generalize this result and show that every 3-connected claw-free graph
G
such that every locally disconnected vertex lies on some induced cycle of length at least 4 with at most 4 edges contained in some triangle of
G
is Hamiltonian. It is best possible in some sense.</description><identifier>ISSN: 0911-0119</identifier><identifier>EISSN: 1435-5914</identifier><identifier>DOI: 10.1007/s00373-013-1343-7</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Combinatorial analysis ; Combinatorics ; Disengaging ; Engineering Design ; Graph theory ; Graphs ; Mathematics ; Mathematics and Statistics ; Original Paper ; Triangles</subject><ispartof>Graphs and combinatorics, 2014-09, Vol.30 (5), p.1261-1269</ispartof><rights>Springer Japan 2013</rights><rights>Springer Japan 2014</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c382t-116bc65519162ef31f0b6d75114f22f8f8e68cb010af7cc5a8fbc44d52b640383</citedby><cites>FETCH-LOGICAL-c382t-116bc65519162ef31f0b6d75114f22f8f8e68cb010af7cc5a8fbc44d52b640383</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/s00373-013-1343-7$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00373-013-1343-7$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Tian, Runli</creatorcontrib><creatorcontrib>Xiong, Liming</creatorcontrib><creatorcontrib>Niu, Zhaohong</creatorcontrib><title>On Hamiltonicity of 3-Connected Claw-Free Graphs</title><title>Graphs and combinatorics</title><addtitle>Graphs and Combinatorics</addtitle><description>Lai, Shao and Zhan (J Graph Theory 48:142–146,
2005
) showed that every 3-connected
N
2
-locally connected claw-free graph is Hamiltonian. In this paper, we generalize this result and show that every 3-connected claw-free graph
G
such that every locally disconnected vertex lies on some induced cycle of length at least 4 with at most 4 edges contained in some triangle of
G
is Hamiltonian. It is best possible in some sense.</description><subject>Combinatorial analysis</subject><subject>Combinatorics</subject><subject>Disengaging</subject><subject>Engineering Design</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Triangles</subject><issn>0911-0119</issn><issn>1435-5914</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp1kE1Lw0AURQdRsFZ_gLuAGzej781XkqUE2wqFbnQ9TCYzmpJm6kyK9N-bEhciuHqLe-7lcQi5RXhAgPwxAfCcU0BOkQtO8zMyQ8EllSWKczKDEnFMsbwkVyltAUCigBmBTZ-tzK7thtC3th2OWfAZp1Xoe2cH12RVZ77oIjqXLaPZf6RrcuFNl9zNz52Tt8Xza7Wi683ypXpaU8sLNlBEVVslJZaomPMcPdSqySWi8Iz5whdOFbYGBONza6UpfG2FaCSrlQBe8Dm5n3b3MXweXBr0rk3WdZ3pXTgkjVLlCCUDOaJ3f9BtOMR-_G6kJFeMM8hHCifKxpBSdF7vY7sz8agR9Mmhnhzq0aE-OdSnDps6aWT7dxd_Lf9b-gazEHCc</recordid><startdate>20140901</startdate><enddate>20140901</enddate><creator>Tian, Runli</creator><creator>Xiong, Liming</creator><creator>Niu, Zhaohong</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>20140901</creationdate><title>On Hamiltonicity of 3-Connected Claw-Free Graphs</title><author>Tian, Runli ; Xiong, Liming ; Niu, Zhaohong</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-116bc65519162ef31f0b6d75114f22f8f8e68cb010af7cc5a8fbc44d52b640383</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>Combinatorial analysis</topic><topic>Combinatorics</topic><topic>Disengaging</topic><topic>Engineering Design</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Triangles</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Tian, Runli</creatorcontrib><creatorcontrib>Xiong, Liming</creatorcontrib><creatorcontrib>Niu, Zhaohong</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>Tian, Runli</au><au>Xiong, Liming</au><au>Niu, Zhaohong</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Hamiltonicity of 3-Connected Claw-Free Graphs</atitle><jtitle>Graphs and combinatorics</jtitle><stitle>Graphs and Combinatorics</stitle><date>2014-09-01</date><risdate>2014</risdate><volume>30</volume><issue>5</issue><spage>1261</spage><epage>1269</epage><pages>1261-1269</pages><issn>0911-0119</issn><eissn>1435-5914</eissn><abstract>Lai, Shao and Zhan (J Graph Theory 48:142–146,
2005
) showed that every 3-connected
N
2
-locally connected claw-free graph is Hamiltonian. In this paper, we generalize this result and show that every 3-connected claw-free graph
G
such that every locally disconnected vertex lies on some induced cycle of length at least 4 with at most 4 edges contained in some triangle of
G
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| issn | 0911-0119 1435-5914 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1567109205 |
| source | SpringerLink Journals |
| subjects | Combinatorial analysis Combinatorics Disengaging Engineering Design Graph theory Graphs Mathematics Mathematics and Statistics Original Paper Triangles |
| title | On Hamiltonicity of 3-Connected Claw-Free Graphs |
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