Lower bounds on the independence number of certain graphs of odd girth at least seven
Heckman and Thomas [C.C. Heckman, R. Thomas, A new proof of the independence ratio of triangle-free cubic graphs, Discrete Math. 233 (2001) 233–237] proved that every connected subcubic triangle-free graph G has an independent set of order at least ( 4 n ( G ) − m ( G ) − 1 ) / 7 where n ( G ) and m...
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| Veröffentlicht in: | Discrete Applied Mathematics 2011, Vol.159 (2), p.143-151 |
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| creator | Pedersen, Anders Sune Rautenbach, Dieter Regen, Friedrich |
| description | Heckman and Thomas [C.C. Heckman, R. Thomas, A new proof of the independence ratio of triangle-free cubic graphs, Discrete Math. 233 (2001) 233–237] proved that every connected subcubic triangle-free graph
G
has an independent set of order at least
(
4
n
(
G
)
−
m
(
G
)
−
1
)
/
7
where
n
(
G
)
and
m
(
G
)
denote the order and size of
G
, respectively. We conjecture that every connected subcubic graph
G
of odd girth at least seven has an independent set of order at least
(
5
n
(
G
)
−
m
(
G
)
−
1
)
/
9
and verify our conjecture under some additional technical assumptions. |
| doi_str_mv | 10.1016/j.dam.2010.10.011 |
| format | Article |
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G
has an independent set of order at least
(
4
n
(
G
)
−
m
(
G
)
−
1
)
/
7
where
n
(
G
)
and
m
(
G
)
denote the order and size of
G
, respectively. We conjecture that every connected subcubic graph
G
of odd girth at least seven has an independent set of order at least
(
5
n
(
G
)
−
m
(
G
)
−
1
)
/
9
and verify our conjecture under some additional technical assumptions.</description><identifier>ISSN: 0166-218X</identifier><identifier>EISSN: 1872-6771</identifier><identifier>DOI: 10.1016/j.dam.2010.10.011</identifier><identifier>CODEN: DAMADU</identifier><language>eng</language><publisher>Kidlington: Elsevier B.V</publisher><subject>Algorithmics. Computability. Computer arithmetics ; Applied sciences ; Combinatorics ; Combinatorics. Ordered structures ; Computer science; control theory; systems ; Exact sciences and technology ; Graphs ; Independence ; Information retrieval. Graph ; Lower bounds ; Mathematical analysis ; Mathematics ; Odd girth ; Order, lattices, ordered algebraic structures ; Proving ; Sciences and techniques of general use ; Stability ; Theoretical computing</subject><ispartof>Discrete Applied Mathematics, 2011, Vol.159 (2), p.143-151</ispartof><rights>2010 Elsevier B.V.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c403t-ed11d25dc77335ee9d12cfefab93a3faf55f2c5125613f802c967f437ae4ec5e3</citedby><cites>FETCH-LOGICAL-c403t-ed11d25dc77335ee9d12cfefab93a3faf55f2c5125613f802c967f437ae4ec5e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0166218X10003537$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,4010,27900,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23817371$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Pedersen, Anders Sune</creatorcontrib><creatorcontrib>Rautenbach, Dieter</creatorcontrib><creatorcontrib>Regen, Friedrich</creatorcontrib><title>Lower bounds on the independence number of certain graphs of odd girth at least seven</title><title>Discrete Applied Mathematics</title><description>Heckman and Thomas [C.C. Heckman, R. Thomas, A new proof of the independence ratio of triangle-free cubic graphs, Discrete Math. 233 (2001) 233–237] proved that every connected subcubic triangle-free graph
G
has an independent set of order at least
(
4
n
(
G
)
−
m
(
G
)
−
1
)
/
7
where
n
(
G
)
and
m
(
G
)
denote the order and size of
G
, respectively. We conjecture that every connected subcubic graph
G
of odd girth at least seven has an independent set of order at least
(
5
n
(
G
)
−
m
(
G
)
−
1
)
/
9
and verify our conjecture under some additional technical assumptions.</description><subject>Algorithmics. Computability. Computer arithmetics</subject><subject>Applied sciences</subject><subject>Combinatorics</subject><subject>Combinatorics. Ordered structures</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Graphs</subject><subject>Independence</subject><subject>Information retrieval. Graph</subject><subject>Lower bounds</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Odd girth</subject><subject>Order, lattices, ordered algebraic structures</subject><subject>Proving</subject><subject>Sciences and techniques of general use</subject><subject>Stability</subject><subject>Theoretical computing</subject><issn>0166-218X</issn><issn>1872-6771</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQQIMoWKs_wFsugpetmaS7afEk4hcUvCh4C2kysSnbpCa7iv_erC0evcwww5sZ5hFyDmwCDJqr9cTqzYSz33rCAA7ICGaSV42UcEhGhWkqDrO3Y3KS85oxBqUakddF_MJEl7EPNtMYaLdC6oPFLZYQDNLQb5aFiI4aTJ32gb4nvV3loROtpe8-dSuqO9qizh3N-InhlBw53WY82-cxeb2_e7l9rBbPD0-3N4vKTJnoKrQAltfWSClEjTi3wI1Dp5dzoYXTrq4dNzXwugHhZoybeSPdVEiNUzQ1ijG53O3dpvjRY-7UxmeDbasDxj4raCTwaQO8KSjsUJNizgmd2ia_0elbAVODQrVWRaEaFA6torDMXOzX62x065IOxue_QS5mIIUcuOsdh-XXT49JZeMHedYnNJ2y0f9z5QeGBIaG</recordid><startdate>2011</startdate><enddate>2011</enddate><creator>Pedersen, Anders Sune</creator><creator>Rautenbach, Dieter</creator><creator>Regen, Friedrich</creator><general>Elsevier B.V</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>2011</creationdate><title>Lower bounds on the independence number of certain graphs of odd girth at least seven</title><author>Pedersen, Anders Sune ; Rautenbach, Dieter ; Regen, Friedrich</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c403t-ed11d25dc77335ee9d12cfefab93a3faf55f2c5125613f802c967f437ae4ec5e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Algorithmics. Computability. Computer arithmetics</topic><topic>Applied sciences</topic><topic>Combinatorics</topic><topic>Combinatorics. Ordered structures</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Graphs</topic><topic>Independence</topic><topic>Information retrieval. Graph</topic><topic>Lower bounds</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Odd girth</topic><topic>Order, lattices, ordered algebraic structures</topic><topic>Proving</topic><topic>Sciences and techniques of general use</topic><topic>Stability</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Pedersen, Anders Sune</creatorcontrib><creatorcontrib>Rautenbach, Dieter</creatorcontrib><creatorcontrib>Regen, Friedrich</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</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>Discrete Applied Mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Pedersen, Anders Sune</au><au>Rautenbach, Dieter</au><au>Regen, Friedrich</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Lower bounds on the independence number of certain graphs of odd girth at least seven</atitle><jtitle>Discrete Applied Mathematics</jtitle><date>2011</date><risdate>2011</risdate><volume>159</volume><issue>2</issue><spage>143</spage><epage>151</epage><pages>143-151</pages><issn>0166-218X</issn><eissn>1872-6771</eissn><coden>DAMADU</coden><abstract>Heckman and Thomas [C.C. Heckman, R. Thomas, A new proof of the independence ratio of triangle-free cubic graphs, Discrete Math. 233 (2001) 233–237] proved that every connected subcubic triangle-free graph
G
has an independent set of order at least
(
4
n
(
G
)
−
m
(
G
)
−
1
)
/
7
where
n
(
G
)
and
m
(
G
)
denote the order and size of
G
, respectively. We conjecture that every connected subcubic graph
G
of odd girth at least seven has an independent set of order at least
(
5
n
(
G
)
−
m
(
G
)
−
1
)
/
9
and verify our conjecture under some additional technical assumptions.</abstract><cop>Kidlington</cop><pub>Elsevier B.V</pub><doi>10.1016/j.dam.2010.10.011</doi><tpages>9</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
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| ispartof | Discrete Applied Mathematics, 2011, Vol.159 (2), p.143-151 |
| issn | 0166-218X 1872-6771 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1671246126 |
| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Algorithmics. Computability. Computer arithmetics Applied sciences Combinatorics Combinatorics. Ordered structures Computer science control theory systems Exact sciences and technology Graphs Independence Information retrieval. Graph Lower bounds Mathematical analysis Mathematics Odd girth Order, lattices, ordered algebraic structures Proving Sciences and techniques of general use Stability Theoretical computing |
| title | Lower bounds on the independence number of certain graphs of odd girth at least seven |
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