Injective colorings of sparse graphs
Let mad ( G ) denote the maximum average degree (over all subgraphs) of G and let χ i ( G ) denote the injective chromatic number of G . We prove that if mad ( G ) ≤ 5 2 , then χ i ( G ) ≤ Δ ( G ) + 1 ; and if mad ( G ) < 42 19 , then χ i ( G ) = Δ ( G ) . Suppose that G is a planar graph with gi...
Gespeichert in:
| Veröffentlicht in: | Discrete mathematics 2010-11, Vol.310 (21), p.2965-2973 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 2973 |
|---|---|
| container_issue | 21 |
| container_start_page | 2965 |
| container_title | Discrete mathematics |
| container_volume | 310 |
| creator | Cranston, Daniel W. Kim, Seog-Jin Yu, Gexin |
| description | Let
mad
(
G
)
denote the maximum average degree (over all subgraphs) of
G
and let
χ
i
(
G
)
denote the injective chromatic number of
G
. We prove that if
mad
(
G
)
≤
5
2
, then
χ
i
(
G
)
≤
Δ
(
G
)
+
1
; and if
mad
(
G
)
<
42
19
, then
χ
i
(
G
)
=
Δ
(
G
)
. Suppose that
G
is a planar graph with girth
g
(
G
)
and
Δ
(
G
)
≥
4
. We prove that if
g
(
G
)
≥
9
, then
χ
i
(
G
)
≤
Δ
(
G
)
+
1
; similarly, if
g
(
G
)
≥
13
, then
χ
i
(
G
)
=
Δ
(
G
)
. |
| doi_str_mv | 10.1016/j.disc.2010.07.003 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_849451737</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0012365X10002736</els_id><sourcerecordid>849451737</sourcerecordid><originalsourceid>FETCH-LOGICAL-c362t-c7152ffc33b2c81de33e3cede98e22cc510cc78f29909a335d1601ee5437999c3</originalsourceid><addsrcrecordid>eNp9kM1Lw0AQxRdRsFb_AU85KJ4S96PJ7oIXKX4UCl4UelvWyaRuSJO60xb8793S4tHTMMN7b3g_xq4FLwQX1X1b1IGgkDwduC44VydsJIyWeWXE4pSNOBcyV1W5OGcXRC1Pe6XMiN3M-hZhE3aYwdANMfRLyoYmo7WPhNky-vUXXbKzxneEV8c5Zh_PT-_T13z-9jKbPs5zUJXc5KBFKZsGlPqUYESNSqECrNEalBKgFBxAm0Zay61XqqxFxQViOVHaWgtqzO4Oues4fG-RNm6VWmHX-R6HLTkzsZNSaKWTUh6UEAeiiI1bx7Dy8ccJ7vZEXOv2RNyeiOPaJSLJdHuM9wS-a6LvIdCfUyoppCl50j0cdJi67gJGRxCwT01CTKxcPYT_3vwC-Ux1gQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>849451737</pqid></control><display><type>article</type><title>Injective colorings of sparse graphs</title><source>Elsevier ScienceDirect Journals</source><source>Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals</source><creator>Cranston, Daniel W. ; Kim, Seog-Jin ; Yu, Gexin</creator><creatorcontrib>Cranston, Daniel W. ; Kim, Seog-Jin ; Yu, Gexin</creatorcontrib><description>Let
mad
(
G
)
denote the maximum average degree (over all subgraphs) of
G
and let
χ
i
(
G
)
denote the injective chromatic number of
G
. We prove that if
mad
(
G
)
≤
5
2
, then
χ
i
(
G
)
≤
Δ
(
G
)
+
1
; and if
mad
(
G
)
<
42
19
, then
χ
i
(
G
)
=
Δ
(
G
)
. Suppose that
G
is a planar graph with girth
g
(
G
)
and
Δ
(
G
)
≥
4
. We prove that if
g
(
G
)
≥
9
, then
χ
i
(
G
)
≤
Δ
(
G
)
+
1
; similarly, if
g
(
G
)
≥
13
, then
χ
i
(
G
)
=
Δ
(
G
)
.</description><identifier>ISSN: 0012-365X</identifier><identifier>EISSN: 1872-681X</identifier><identifier>DOI: 10.1016/j.disc.2010.07.003</identifier><identifier>CODEN: DSMHA4</identifier><language>eng</language><publisher>Kidlington: Elsevier B.V</publisher><subject>Algebra ; Applied sciences ; Coloring ; Combinatorics ; Combinatorics. Ordered structures ; Computer science; control theory; systems ; Exact sciences and technology ; Graph theory ; Graphs ; Information retrieval. Graph ; Injective coloring ; Mathematical analysis ; Mathematics ; Maximum average degree ; Planar graph ; Sciences and techniques of general use ; Theoretical computing</subject><ispartof>Discrete mathematics, 2010-11, Vol.310 (21), p.2965-2973</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-c7152ffc33b2c81de33e3cede98e22cc510cc78f29909a335d1601ee5437999c3</citedby><cites>FETCH-LOGICAL-c362t-c7152ffc33b2c81de33e3cede98e22cc510cc78f29909a335d1601ee5437999c3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0012365X10002736$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23212850$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Cranston, Daniel W.</creatorcontrib><creatorcontrib>Kim, Seog-Jin</creatorcontrib><creatorcontrib>Yu, Gexin</creatorcontrib><title>Injective colorings of sparse graphs</title><title>Discrete mathematics</title><description>Let
mad
(
G
)
denote the maximum average degree (over all subgraphs) of
G
and let
χ
i
(
G
)
denote the injective chromatic number of
G
. We prove that if
mad
(
G
)
≤
5
2
, then
χ
i
(
G
)
≤
Δ
(
G
)
+
1
; and if
mad
(
G
)
<
42
19
, then
χ
i
(
G
)
=
Δ
(
G
)
. Suppose that
G
is a planar graph with girth
g
(
G
)
and
Δ
(
G
)
≥
4
. We prove that if
g
(
G
)
≥
9
, then
χ
i
(
G
)
≤
Δ
(
G
)
+
1
; similarly, if
g
(
G
)
≥
13
, then
χ
i
(
G
)
=
Δ
(
G
)
.</description><subject>Algebra</subject><subject>Applied sciences</subject><subject>Coloring</subject><subject>Combinatorics</subject><subject>Combinatorics. Ordered structures</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Information retrieval. Graph</subject><subject>Injective coloring</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Maximum average degree</subject><subject>Planar graph</subject><subject>Sciences and techniques of general use</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>eNp9kM1Lw0AQxRdRsFb_AU85KJ4S96PJ7oIXKX4UCl4UelvWyaRuSJO60xb8793S4tHTMMN7b3g_xq4FLwQX1X1b1IGgkDwduC44VydsJIyWeWXE4pSNOBcyV1W5OGcXRC1Pe6XMiN3M-hZhE3aYwdANMfRLyoYmo7WPhNky-vUXXbKzxneEV8c5Zh_PT-_T13z-9jKbPs5zUJXc5KBFKZsGlPqUYESNSqECrNEalBKgFBxAm0Zay61XqqxFxQViOVHaWgtqzO4Oues4fG-RNm6VWmHX-R6HLTkzsZNSaKWTUh6UEAeiiI1bx7Dy8ccJ7vZEXOv2RNyeiOPaJSLJdHuM9wS-a6LvIdCfUyoppCl50j0cdJi67gJGRxCwT01CTKxcPYT_3vwC-Ux1gQ</recordid><startdate>20101106</startdate><enddate>20101106</enddate><creator>Cranston, Daniel W.</creator><creator>Kim, Seog-Jin</creator><creator>Yu, Gexin</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>20101106</creationdate><title>Injective colorings of sparse graphs</title><author>Cranston, Daniel W. ; Kim, Seog-Jin ; Yu, Gexin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c362t-c7152ffc33b2c81de33e3cede98e22cc510cc78f29909a335d1601ee5437999c3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Algebra</topic><topic>Applied sciences</topic><topic>Coloring</topic><topic>Combinatorics</topic><topic>Combinatorics. Ordered structures</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Information retrieval. Graph</topic><topic>Injective coloring</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Maximum average degree</topic><topic>Planar graph</topic><topic>Sciences and techniques of general use</topic><topic>Theoretical computing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Cranston, Daniel W.</creatorcontrib><creatorcontrib>Kim, Seog-Jin</creatorcontrib><creatorcontrib>Yu, Gexin</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>Cranston, Daniel W.</au><au>Kim, Seog-Jin</au><au>Yu, Gexin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Injective colorings of sparse graphs</atitle><jtitle>Discrete mathematics</jtitle><date>2010-11-06</date><risdate>2010</risdate><volume>310</volume><issue>21</issue><spage>2965</spage><epage>2973</epage><pages>2965-2973</pages><issn>0012-365X</issn><eissn>1872-681X</eissn><coden>DSMHA4</coden><abstract>Let
mad
(
G
)
denote the maximum average degree (over all subgraphs) of
G
and let
χ
i
(
G
)
denote the injective chromatic number of
G
. We prove that if
mad
(
G
)
≤
5
2
, then
χ
i
(
G
)
≤
Δ
(
G
)
+
1
; and if
mad
(
G
)
<
42
19
, then
χ
i
(
G
)
=
Δ
(
G
)
. Suppose that
G
is a planar graph with girth
g
(
G
)
and
Δ
(
G
)
≥
4
. We prove that if
g
(
G
)
≥
9
, then
χ
i
(
G
)
≤
Δ
(
G
)
+
1
; similarly, if
g
(
G
)
≥
13
, then
χ
i
(
G
)
=
Δ
(
G
)
.</abstract><cop>Kidlington</cop><pub>Elsevier B.V</pub><doi>10.1016/j.disc.2010.07.003</doi><tpages>9</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0012-365X |
| ispartof | Discrete mathematics, 2010-11, Vol.310 (21), p.2965-2973 |
| issn | 0012-365X 1872-681X |
| language | eng |
| recordid | cdi_proquest_miscellaneous_849451737 |
| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Algebra Applied sciences Coloring Combinatorics Combinatorics. Ordered structures Computer science control theory systems Exact sciences and technology Graph theory Graphs Information retrieval. Graph Injective coloring Mathematical analysis Mathematics Maximum average degree Planar graph Sciences and techniques of general use Theoretical computing |
| title | Injective colorings of sparse graphs |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-09T01%3A22%3A26IST&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=Injective%20colorings%20of%20sparse%20graphs&rft.jtitle=Discrete%20mathematics&rft.au=Cranston,%20Daniel%20W.&rft.date=2010-11-06&rft.volume=310&rft.issue=21&rft.spage=2965&rft.epage=2973&rft.pages=2965-2973&rft.issn=0012-365X&rft.eissn=1872-681X&rft.coden=DSMHA4&rft_id=info:doi/10.1016/j.disc.2010.07.003&rft_dat=%3Cproquest_cross%3E849451737%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=849451737&rft_id=info:pmid/&rft_els_id=S0012365X10002736&rfr_iscdi=true |