Backbone Coloring for Triangle-free Planar Graphs
Let G be a graph and H a subgraph of G. A backbone-k-coloring of （G, H） is a mapping f： V（G） → {1,2,…,k} such that If（u）- f（v）｜ ≥ 2 if uv ∈ E（H） and ｜f（u）- f（v） ｜ ≥ 1 if uv ∈ E（G）／E（H）. The backbone chromatic number of （G, H） denoted by Xb（G, H） is the smallest integer k such that （G, H） has a backb...
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| Veröffentlicht in: | Acta Mathematicae Applicatae Sinica 2017-07, Vol.33 (3), p.819-824 |
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| container_title | Acta Mathematicae Applicatae Sinica |
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| creator | Bu, Yue-hua Zhang, Shui-ming |
| description | Let G be a graph and H a subgraph of G. A backbone-k-coloring of （G, H） is a mapping f： V（G） → {1,2,…,k} such that If（u）- f（v）｜ ≥ 2 if uv ∈ E（H） and ｜f（u）- f（v） ｜ ≥ 1 if uv ∈ E（G）／E（H）. The backbone chromatic number of （G, H） denoted by Xb（G, H） is the smallest integer k such that （G, H） has a backbone-k-coloring. In this paper, we prove that if G is either a connected triangle-free planar graph or a connected graph with mad（G） 〈 3, then there exists a spanning tree T of G such that Xb（G, T） ≤ 4. |
| doi_str_mv | 10.1007/s10255-017-0700-3 |
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In this paper, we prove that if G is either a connected triangle-free planar graph or a connected graph with mad（G） 〈 3, then there exists a spanning tree T of G such that Xb（G, T） ≤ 4.</description><edition>English series</edition><identifier>ISSN: 0168-9673</identifier><identifier>EISSN: 1618-3932</identifier><identifier>DOI: 10.1007/s10255-017-0700-3</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Applications of Mathematics ; Backbone ; Coloring ; Math Applications in Computer Science ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Theoretical ; 三角形 ; 主干 ; 子图 ; 平面图 ; 映射 ; 着色 ; 连通图</subject><ispartof>Acta Mathematicae Applicatae Sinica, 2017-07, Vol.33 (3), p.819-824</ispartof><rights>Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c295t-b5c0f5098ace6203a6a4334ca921e79713337c85c446d8c5450b83b4ce8d836f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttp://image.cqvip.com/vip1000/qk/85829X/85829X.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10255-017-0700-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10255-017-0700-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Bu, Yue-hua</creatorcontrib><creatorcontrib>Zhang, Shui-ming</creatorcontrib><title>Backbone Coloring for Triangle-free Planar Graphs</title><title>Acta Mathematicae Applicatae Sinica</title><addtitle>Acta Math. 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In this paper, we prove that if G is either a connected triangle-free planar graph or a connected graph with mad（G） 〈 3, then there exists a spanning tree T of G such that Xb（G, T） ≤ 4.</description><subject>Applications of Mathematics</subject><subject>Backbone</subject><subject>Coloring</subject><subject>Math Applications in Computer Science</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Theoretical</subject><subject>三角形</subject><subject>主干</subject><subject>子图</subject><subject>平面图</subject><subject>映射</subject><subject>着色</subject><subject>连通图</subject><issn>0168-9673</issn><issn>1618-3932</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kD1PwzAYhC0EEqXwA9gimA2v_cZfI1RQkCrBUGbLcZ1-EOLUbgf-PalSISamW-650x0h1wzuGIC6zwy4EBSYoqAAKJ6QEZNMUzTIT8kImNTUSIXn5CLnDfRGlGpE2KPzn1VsQzGJTUzrdlnUMRXztHbtsgm0TiEU741rXSqmyXWrfEnOatfkcHXUMfl4fppPXujsbfo6eZhRz43Y0Up4qAUY7XyQHNBJVyKW3hnOgjKKIaLyWviylAvtRSmg0liVPuiFRlnjmNwOuV2K233IO7uJ-9T2lZYZrowptRC9iw0un2LOKdS2S-svl74tA3t4xg7P2H6wPTxjsWf4wOTuMDikP8n_QDfHolVsl9ue-22SiksutDD4A6ZGbwQ</recordid><startdate>20170701</startdate><enddate>20170701</enddate><creator>Bu, Yue-hua</creator><creator>Zhang, Shui-ming</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170701</creationdate><title>Backbone Coloring for Triangle-free Planar Graphs</title><author>Bu, Yue-hua ; Zhang, Shui-ming</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c295t-b5c0f5098ace6203a6a4334ca921e79713337c85c446d8c5450b83b4ce8d836f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Applications of Mathematics</topic><topic>Backbone</topic><topic>Coloring</topic><topic>Math Applications in Computer Science</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Theoretical</topic><topic>三角形</topic><topic>主干</topic><topic>子图</topic><topic>平面图</topic><topic>映射</topic><topic>着色</topic><topic>连通图</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bu, Yue-hua</creatorcontrib><creatorcontrib>Zhang, Shui-ming</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><jtitle>Acta Mathematicae Applicatae Sinica</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bu, Yue-hua</au><au>Zhang, Shui-ming</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Backbone Coloring for Triangle-free Planar Graphs</atitle><jtitle>Acta Mathematicae Applicatae Sinica</jtitle><stitle>Acta Math. 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| subjects | Applications of Mathematics Backbone Coloring Math Applications in Computer Science Mathematical and Computational Physics Mathematics Mathematics and Statistics Theoretical 三角形 主干 子图 平面图 映射 着色 连通图 |
| title | Backbone Coloring for Triangle-free Planar Graphs |
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