On 3-edge-connected supereulerian graphs in graph family C ( l , k )
Let l > 0 and k ≥ 0 be two integers. Denote by C ( l , k ) the family of 2-edge-connected graphs such that a graph G ∈ C ( l , k ) if and only if for every bond S ⊂ E ( G ) with | S | ≤ 3 , each component of G − S has order at least ( | V ( G ) | − k ) / l . In this paper we prove that if a 3-edg...
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| Veröffentlicht in: | Discrete mathematics 2010-09, Vol.310 (17), p.2455-2459 |
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| container_title | Discrete mathematics |
| container_volume | 310 |
| creator | Li, Xiaomin Li, Dengxin Lai, Hong-Jian |
| description | Let
l
>
0
and
k
≥
0
be two integers. Denote by
C
(
l
,
k
)
the family of 2-edge-connected graphs such that a graph
G
∈
C
(
l
,
k
)
if and only if for every bond
S
⊂
E
(
G
)
with
|
S
|
≤
3
, each component of
G
−
S
has order at least
(
|
V
(
G
)
|
−
k
)
/
l
. In this paper we prove that if a 3-edge-connected graph
G
∈
C
(
12
,
1
)
, then
G
is supereulerian if and only if
G
cannot be contracted to the Petersen graph. Our result extends some results by Chen and by Niu and Xiong. Some applications are also discussed. |
| doi_str_mv | 10.1016/j.disc.2010.05.021 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_753686561</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0012365X10001810</els_id><sourcerecordid>753686561</sourcerecordid><originalsourceid>FETCH-LOGICAL-c362t-c062dc8480fece5a8d6d0daffff7bd301b882ede806a89e82b66f31203d2b2963</originalsourceid><addsrcrecordid>eNp9kE1LAzEQhoMoWKt_wFMuooK7TpJuGsGL1E8o9KLQW8gmszV1u7smXaH_3pQWj85lPnjnHeYh5JxBzoDJ22XufLQ5hzSAIgfODsiAqTHPpGLzQzIAYDwTspgfk5MYl5B6KdSAPM4aKjJ0C8xs2zRo1-ho7DsM2NcYvGnoIpjuM1K_r2hlVr7e0Am9ojW9oV_0-pQcVaaOeLbPQ_Lx_PQ-ec2ms5e3ycM0s0LydWZBcmfVSEGFFgujnHTgTJViXDoBrFSKo0MF0qg7VLyUshKMg3C85HdSDMnlzrcL7XePca1X6Wusa9Ng20c9LoRUspAsKflOaUMbY8BKd8GvTNhoBnpLTC_1lpjeEtNQ6EQsLV3s7U20pq6CaayPf5tcAB-N1Cjp7nc6TL_-eAw6Wo-NRedDAqhd6_878wuqUH-c</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>753686561</pqid></control><display><type>article</type><title>On 3-edge-connected supereulerian graphs in graph family C ( l , k )</title><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><source>ScienceDirect Journals (5 years ago - present)</source><creator>Li, Xiaomin ; Li, Dengxin ; Lai, Hong-Jian</creator><creatorcontrib>Li, Xiaomin ; Li, Dengxin ; Lai, Hong-Jian</creatorcontrib><description>Let
l
>
0
and
k
≥
0
be two integers. Denote by
C
(
l
,
k
)
the family of 2-edge-connected graphs such that a graph
G
∈
C
(
l
,
k
)
if and only if for every bond
S
⊂
E
(
G
)
with
|
S
|
≤
3
, each component of
G
−
S
has order at least
(
|
V
(
G
)
|
−
k
)
/
l
. In this paper we prove that if a 3-edge-connected graph
G
∈
C
(
12
,
1
)
, then
G
is supereulerian if and only if
G
cannot be contracted to the Petersen graph. Our result extends some results by Chen and by Niu and Xiong. Some applications are also discussed.</description><identifier>ISSN: 0012-365X</identifier><identifier>EISSN: 1872-681X</identifier><identifier>DOI: 10.1016/j.disc.2010.05.021</identifier><identifier>CODEN: DSMHA4</identifier><language>eng</language><publisher>Kidlington: Elsevier B.V</publisher><subject>Algebra ; Applied sciences ; Bonding ; Collapsible graphs ; Combinatorics ; Combinatorics. Ordered structures ; Computer science; control theory; systems ; Edge-cut ; Exact sciences and technology ; Graphs ; Information retrieval. Graph ; Integers ; Mathematical analysis ; Mathematics ; Petersen graph ; Reduction ; Sciences and techniques of general use ; Supereulerian graphs ; Theoretical computing</subject><ispartof>Discrete mathematics, 2010-09, Vol.310 (17), p.2455-2459</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-c362t-c062dc8480fece5a8d6d0daffff7bd301b882ede806a89e82b66f31203d2b2963</citedby><cites>FETCH-LOGICAL-c362t-c062dc8480fece5a8d6d0daffff7bd301b882ede806a89e82b66f31203d2b2963</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.disc.2010.05.021$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,3548,27923,27924,45994</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23024484$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Li, Xiaomin</creatorcontrib><creatorcontrib>Li, Dengxin</creatorcontrib><creatorcontrib>Lai, Hong-Jian</creatorcontrib><title>On 3-edge-connected supereulerian graphs in graph family C ( l , k )</title><title>Discrete mathematics</title><description>Let
l
>
0
and
k
≥
0
be two integers. Denote by
C
(
l
,
k
)
the family of 2-edge-connected graphs such that a graph
G
∈
C
(
l
,
k
)
if and only if for every bond
S
⊂
E
(
G
)
with
|
S
|
≤
3
, each component of
G
−
S
has order at least
(
|
V
(
G
)
|
−
k
)
/
l
. In this paper we prove that if a 3-edge-connected graph
G
∈
C
(
12
,
1
)
, then
G
is supereulerian if and only if
G
cannot be contracted to the Petersen graph. Our result extends some results by Chen and by Niu and Xiong. Some applications are also discussed.</description><subject>Algebra</subject><subject>Applied sciences</subject><subject>Bonding</subject><subject>Collapsible graphs</subject><subject>Combinatorics</subject><subject>Combinatorics. Ordered structures</subject><subject>Computer science; control theory; systems</subject><subject>Edge-cut</subject><subject>Exact sciences and technology</subject><subject>Graphs</subject><subject>Information retrieval. Graph</subject><subject>Integers</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Petersen graph</subject><subject>Reduction</subject><subject>Sciences and techniques of general use</subject><subject>Supereulerian graphs</subject><subject>Theoretical computing</subject><issn>0012-365X</issn><issn>1872-681X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKt_wFMuooK7TpJuGsGL1E8o9KLQW8gmszV1u7smXaH_3pQWj85lPnjnHeYh5JxBzoDJ22XufLQ5hzSAIgfODsiAqTHPpGLzQzIAYDwTspgfk5MYl5B6KdSAPM4aKjJ0C8xs2zRo1-ho7DsM2NcYvGnoIpjuM1K_r2hlVr7e0Am9ojW9oV_0-pQcVaaOeLbPQ_Lx_PQ-ec2ms5e3ycM0s0LydWZBcmfVSEGFFgujnHTgTJViXDoBrFSKo0MF0qg7VLyUshKMg3C85HdSDMnlzrcL7XePca1X6Wusa9Ng20c9LoRUspAsKflOaUMbY8BKd8GvTNhoBnpLTC_1lpjeEtNQ6EQsLV3s7U20pq6CaayPf5tcAB-N1Cjp7nc6TL_-eAw6Wo-NRedDAqhd6_878wuqUH-c</recordid><startdate>20100928</startdate><enddate>20100928</enddate><creator>Li, Xiaomin</creator><creator>Li, Dengxin</creator><creator>Lai, Hong-Jian</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>20100928</creationdate><title>On 3-edge-connected supereulerian graphs in graph family C ( l , k )</title><author>Li, Xiaomin ; Li, Dengxin ; Lai, Hong-Jian</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c362t-c062dc8480fece5a8d6d0daffff7bd301b882ede806a89e82b66f31203d2b2963</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Algebra</topic><topic>Applied sciences</topic><topic>Bonding</topic><topic>Collapsible graphs</topic><topic>Combinatorics</topic><topic>Combinatorics. Ordered structures</topic><topic>Computer science; control theory; systems</topic><topic>Edge-cut</topic><topic>Exact sciences and technology</topic><topic>Graphs</topic><topic>Information retrieval. Graph</topic><topic>Integers</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Petersen graph</topic><topic>Reduction</topic><topic>Sciences and techniques of general use</topic><topic>Supereulerian graphs</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Xiaomin</creatorcontrib><creatorcontrib>Li, Dengxin</creatorcontrib><creatorcontrib>Lai, Hong-Jian</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 mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Xiaomin</au><au>Li, Dengxin</au><au>Lai, Hong-Jian</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On 3-edge-connected supereulerian graphs in graph family C ( l , k )</atitle><jtitle>Discrete mathematics</jtitle><date>2010-09-28</date><risdate>2010</risdate><volume>310</volume><issue>17</issue><spage>2455</spage><epage>2459</epage><pages>2455-2459</pages><issn>0012-365X</issn><eissn>1872-681X</eissn><coden>DSMHA4</coden><abstract>Let
l
>
0
and
k
≥
0
be two integers. Denote by
C
(
l
,
k
)
the family of 2-edge-connected graphs such that a graph
G
∈
C
(
l
,
k
)
if and only if for every bond
S
⊂
E
(
G
)
with
|
S
|
≤
3
, each component of
G
−
S
has order at least
(
|
V
(
G
)
|
−
k
)
/
l
. In this paper we prove that if a 3-edge-connected graph
G
∈
C
(
12
,
1
)
, then
G
is supereulerian if and only if
G
cannot be contracted to the Petersen graph. Our result extends some results by Chen and by Niu and Xiong. Some applications are also discussed.</abstract><cop>Kidlington</cop><pub>Elsevier B.V</pub><doi>10.1016/j.disc.2010.05.021</doi><tpages>5</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0012-365X |
| ispartof | Discrete mathematics, 2010-09, Vol.310 (17), p.2455-2459 |
| issn | 0012-365X 1872-681X |
| language | eng |
| recordid | cdi_proquest_miscellaneous_753686561 |
| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; ScienceDirect Journals (5 years ago - present) |
| subjects | Algebra Applied sciences Bonding Collapsible graphs Combinatorics Combinatorics. Ordered structures Computer science control theory systems Edge-cut Exact sciences and technology Graphs Information retrieval. Graph Integers Mathematical analysis Mathematics Petersen graph Reduction Sciences and techniques of general use Supereulerian graphs Theoretical computing |
| title | On 3-edge-connected supereulerian graphs in graph family C ( l , k ) |
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