The thickness and chromatic number of r -inflated graphs
A graph has thickness t if the edges can be decomposed into t and no fewer planar layers. We study one aspect of a generalization of Ringel’s famous Earth–Moon problem: what is the largest chromatic number of any thickness-2 graph? In particular, given a graph G we consider the r -inflation of G and...
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| Veröffentlicht in: | Discrete mathematics 2010-10, Vol.310 (20), p.2725-2734 |
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| container_issue | 20 |
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| container_title | Discrete mathematics |
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| creator | Albertson, Michael O. Boutin, Debra L. Gethner, Ellen |
| description | A graph has thickness
t
if the edges can be decomposed into
t
and no fewer planar layers. We study one aspect of a generalization of Ringel’s famous Earth–Moon problem: what is the largest chromatic number of any thickness-2 graph? In particular, given a graph
G
we consider the
r
-inflation of
G
and find bounds on both the thickness and the chromatic number of the inflated graphs. In some instances, the best possible bounds on both the chromatic number and thickness are achieved. We end with several open problems. |
| doi_str_mv | 10.1016/j.disc.2010.04.019 |
| format | Article |
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t
if the edges can be decomposed into
t
and no fewer planar layers. We study one aspect of a generalization of Ringel’s famous Earth–Moon problem: what is the largest chromatic number of any thickness-2 graph? In particular, given a graph
G
we consider the
r
-inflation of
G
and find bounds on both the thickness and the chromatic number of the inflated graphs. In some instances, the best possible bounds on both the chromatic number and thickness are achieved. We end with several open problems.</description><identifier>ISSN: 0012-365X</identifier><identifier>EISSN: 1872-681X</identifier><identifier>DOI: 10.1016/j.disc.2010.04.019</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>[formula omitted]-inflation ; Arboricity ; Chromatic number ; Decomposition ; Graph coloring ; Graphs ; Independence number ; Mathematical analysis ; Thickness</subject><ispartof>Discrete mathematics, 2010-10, Vol.310 (20), p.2725-2734</ispartof><rights>2010 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c332t-a75e5592c24ba6a279b363f816b22fc531ba8c1d3c2c9ff0a2bb3d4726676dfd3</citedby><cites>FETCH-LOGICAL-c332t-a75e5592c24ba6a279b363f816b22fc531ba8c1d3c2c9ff0a2bb3d4726676dfd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0012365X10001524$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,27903,27904,65309</link.rule.ids></links><search><creatorcontrib>Albertson, Michael O.</creatorcontrib><creatorcontrib>Boutin, Debra L.</creatorcontrib><creatorcontrib>Gethner, Ellen</creatorcontrib><title>The thickness and chromatic number of r -inflated graphs</title><title>Discrete mathematics</title><description>A graph has thickness
t
if the edges can be decomposed into
t
and no fewer planar layers. We study one aspect of a generalization of Ringel’s famous Earth–Moon problem: what is the largest chromatic number of any thickness-2 graph? In particular, given a graph
G
we consider the
r
-inflation of
G
and find bounds on both the thickness and the chromatic number of the inflated graphs. In some instances, the best possible bounds on both the chromatic number and thickness are achieved. We end with several open problems.</description><subject>[formula omitted]-inflation</subject><subject>Arboricity</subject><subject>Chromatic number</subject><subject>Decomposition</subject><subject>Graph coloring</subject><subject>Graphs</subject><subject>Independence number</subject><subject>Mathematical analysis</subject><subject>Thickness</subject><issn>0012-365X</issn><issn>1872-681X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouH78AU-5eWpNJm2aghdZ_IIFLyvsLaTJxGbtx5p0Bf-9Xdazp2GG9xl4H0JuOMs54_Jum7uQbA5sPrAiZ7w-IQuuKsik4ptTsmCMQyZkuTknFylt2bxLoRZErVukUxvs54ApUTM4ats49mYKlg77vsFIR08jzcLgOzOhox_R7Np0Rc686RJe_81L8v70uF6-ZKu359flwyqzQsCUmarEsqzBQtEYaaCqGyGFV1w2AN6WgjdGWe6EBVt7zww0jXBFBVJW0nknLsnt8e8ujl97TJPu56bYdWbAcZ-0Aih5Lep6TsIxaeOYUkSvdzH0Jv5ozvTBkt7qgyV9sKRZoWdLM3R_hHDu8B0w6mQDDhZdiGgn7cbwH_4LHWZwBw</recordid><startdate>20101028</startdate><enddate>20101028</enddate><creator>Albertson, Michael O.</creator><creator>Boutin, Debra L.</creator><creator>Gethner, Ellen</creator><general>Elsevier B.V</general><scope>6I.</scope><scope>AAFTH</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>20101028</creationdate><title>The thickness and chromatic number of r -inflated graphs</title><author>Albertson, Michael O. ; Boutin, Debra L. ; Gethner, Ellen</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c332t-a75e5592c24ba6a279b363f816b22fc531ba8c1d3c2c9ff0a2bb3d4726676dfd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>[formula omitted]-inflation</topic><topic>Arboricity</topic><topic>Chromatic number</topic><topic>Decomposition</topic><topic>Graph coloring</topic><topic>Graphs</topic><topic>Independence number</topic><topic>Mathematical analysis</topic><topic>Thickness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Albertson, Michael O.</creatorcontrib><creatorcontrib>Boutin, Debra L.</creatorcontrib><creatorcontrib>Gethner, Ellen</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</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>Albertson, Michael O.</au><au>Boutin, Debra L.</au><au>Gethner, Ellen</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The thickness and chromatic number of r -inflated graphs</atitle><jtitle>Discrete mathematics</jtitle><date>2010-10-28</date><risdate>2010</risdate><volume>310</volume><issue>20</issue><spage>2725</spage><epage>2734</epage><pages>2725-2734</pages><issn>0012-365X</issn><eissn>1872-681X</eissn><abstract>A graph has thickness
t
if the edges can be decomposed into
t
and no fewer planar layers. We study one aspect of a generalization of Ringel’s famous Earth–Moon problem: what is the largest chromatic number of any thickness-2 graph? In particular, given a graph
G
we consider the
r
-inflation of
G
and find bounds on both the thickness and the chromatic number of the inflated graphs. In some instances, the best possible bounds on both the chromatic number and thickness are achieved. We end with several open problems.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.disc.2010.04.019</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
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| ispartof | Discrete mathematics, 2010-10, Vol.310 (20), p.2725-2734 |
| issn | 0012-365X 1872-681X |
| language | eng |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | [formula omitted]-inflation Arboricity Chromatic number Decomposition Graph coloring Graphs Independence number Mathematical analysis Thickness |
| title | The thickness and chromatic number of r -inflated graphs |
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