The minimum number of Hamilton cycles in a Hamiltonian threshold graph of a prescribed order
We prove that the minimum number of Hamilton cycles in a Hamiltonian threshold graph of order n is 2 ⌊ ( n − 3 ) ∕ 2 ⌋ and this minimum number is attained uniquely by the graph with degree sequence n − 1 , n − 1 , n − 2 , … , ⌈ n ∕ 2 ⌉ , ⌈ n ∕ 2 ⌉ , … , 3,2 of n − 2 distinct degrees. This graph is a...
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| Veröffentlicht in: | Journal of graph theory 2020-02, Vol.93 (2), p.222-229 |
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| container_title | Journal of graph theory |
| container_volume | 93 |
| creator | Qiao, Pu Zhan, Xingzhi |
| description | We prove that the minimum number of Hamilton cycles in a Hamiltonian threshold graph of order
n is
2
⌊
(
n
−
3
)
∕
2
⌋ and this minimum number is attained uniquely by the graph with degree sequence
n
−
1
,
n
−
1
,
n
−
2
,
…
,
⌈
n
∕
2
⌉
,
⌈
n
∕
2
⌉
,
…
,
3,2 of
n
−
2 distinct degrees. This graph is also the unique graph of minimum size among all Hamiltonian threshold graphs of order
n. |
| doi_str_mv | 10.1002/jgt.22483 |
| format | Article |
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n is
2
⌊
(
n
−
3
)
∕
2
⌋ and this minimum number is attained uniquely by the graph with degree sequence
n
−
1
,
n
−
1
,
n
−
2
,
…
,
⌈
n
∕
2
⌉
,
⌈
n
∕
2
⌉
,
…
,
3,2 of
n
−
2 distinct degrees. This graph is also the unique graph of minimum size among all Hamiltonian threshold graphs of order
n.</description><identifier>ISSN: 0364-9024</identifier><identifier>EISSN: 1097-0118</identifier><identifier>DOI: 10.1002/jgt.22483</identifier><language>eng</language><publisher>Hoboken: Wiley Subscription Services, Inc</publisher><subject>Hamiltonian graph ; minimum size ; number of Hamilton cycles ; threshold graph</subject><ispartof>Journal of graph theory, 2020-02, Vol.93 (2), p.222-229</ispartof><rights>2019 Wiley Periodicals, Inc.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2973-9a789f11c71cea7650fbf365fd12e4d44c351dd45ee4356eaa84eefea9b284533</citedby><cites>FETCH-LOGICAL-c2973-9a789f11c71cea7650fbf365fd12e4d44c351dd45ee4356eaa84eefea9b284533</cites><orcidid>0000-0001-8683-6674</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.22483$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fjgt.22483$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1416,27923,27924,45573,45574</link.rule.ids></links><search><creatorcontrib>Qiao, Pu</creatorcontrib><creatorcontrib>Zhan, Xingzhi</creatorcontrib><title>The minimum number of Hamilton cycles in a Hamiltonian threshold graph of a prescribed order</title><title>Journal of graph theory</title><description>We prove that the minimum number of Hamilton cycles in a Hamiltonian threshold graph of order
n is
2
⌊
(
n
−
3
)
∕
2
⌋ and this minimum number is attained uniquely by the graph with degree sequence
n
−
1
,
n
−
1
,
n
−
2
,
…
,
⌈
n
∕
2
⌉
,
⌈
n
∕
2
⌉
,
…
,
3,2 of
n
−
2 distinct degrees. This graph is also the unique graph of minimum size among all Hamiltonian threshold graphs of order
n.</description><subject>Hamiltonian graph</subject><subject>minimum size</subject><subject>number of Hamilton cycles</subject><subject>threshold graph</subject><issn>0364-9024</issn><issn>1097-0118</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp1kEtLAzEUhYMoWKsL_0HAlYtp85rXUoq2SsFN3Qkhk9x0UuZlMoP033fqiDtXFz6-cy4chO4pWVBC2PKw7xeMiYxfoBkleRoRSrNLNCM8EVFOmLhGNyEcyIhjks3Q564EXLvG1UONm6EuwOPW4o2qXdW3DdZHXUHArsHqDzrV4L70EMq2MnjvVVeeMwp3I9PeFWBw6w34W3RlVRXg7vfO0cfL8261ibbv69fV0zbSLE95lKs0yy2lOqUaVJrExBaWJ7E1lIEwQmgeU2NEDCB4nIBSmQCwoPKCZSLmfI4ept7Ot18DhF4e2sE340vJOKNcUEbT0XqcLO3bEDxY2XlXK3-UlMjzeHIcT_6MN7rLyf12FRz_F-XbejclTj-8cPQ</recordid><startdate>202002</startdate><enddate>202002</enddate><creator>Qiao, Pu</creator><creator>Zhan, Xingzhi</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0001-8683-6674</orcidid></search><sort><creationdate>202002</creationdate><title>The minimum number of Hamilton cycles in a Hamiltonian threshold graph of a prescribed order</title><author>Qiao, Pu ; Zhan, Xingzhi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2973-9a789f11c71cea7650fbf365fd12e4d44c351dd45ee4356eaa84eefea9b284533</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Hamiltonian graph</topic><topic>minimum size</topic><topic>number of Hamilton cycles</topic><topic>threshold graph</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Qiao, Pu</creatorcontrib><creatorcontrib>Zhan, Xingzhi</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of graph theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Qiao, Pu</au><au>Zhan, Xingzhi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The minimum number of Hamilton cycles in a Hamiltonian threshold graph of a prescribed order</atitle><jtitle>Journal of graph theory</jtitle><date>2020-02</date><risdate>2020</risdate><volume>93</volume><issue>2</issue><spage>222</spage><epage>229</epage><pages>222-229</pages><issn>0364-9024</issn><eissn>1097-0118</eissn><abstract>We prove that the minimum number of Hamilton cycles in a Hamiltonian threshold graph of order
n is
2
⌊
(
n
−
3
)
∕
2
⌋ and this minimum number is attained uniquely by the graph with degree sequence
n
−
1
,
n
−
1
,
n
−
2
,
…
,
⌈
n
∕
2
⌉
,
⌈
n
∕
2
⌉
,
…
,
3,2 of
n
−
2 distinct degrees. This graph is also the unique graph of minimum size among all Hamiltonian threshold graphs of order
n.</abstract><cop>Hoboken</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/jgt.22483</doi><tpages>8</tpages><orcidid>https://orcid.org/0000-0001-8683-6674</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0364-9024 |
| ispartof | Journal of graph theory, 2020-02, Vol.93 (2), p.222-229 |
| issn | 0364-9024 1097-0118 |
| language | eng |
| recordid | cdi_proquest_journals_2321341217 |
| source | Wiley-Blackwell Journals |
| subjects | Hamiltonian graph minimum size number of Hamilton cycles threshold graph |
| title | The minimum number of Hamilton cycles in a Hamiltonian threshold graph of a prescribed order |
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