λ-Coloring of Graphs
A λ-coloring of a graph G is an assignment of colors from the set 0, ..., λ to the vertices of a graph G such that vertices at distance at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-colorings with small or optimal λ arises in...
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Buchkapitel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 406 |
|---|---|
| container_issue | |
| container_start_page | 395 |
| container_title | |
| container_volume | 1770 |
| creator | Bodlaender, Hans L. Kloks, Ton Tan, Richard B. van Leeuwen, Jan |
| description | A λ-coloring of a graph G is an assignment of colors from the set 0, ..., λ to the vertices of a graph G such that vertices at distance at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-colorings with small or optimal λ arises in the context of radio frequency assignment. We show that the problems of finding the minimum λ for planar graphs, bipartite graphs, chordal graphs and split graphs are NP-Complete. We then give approximation algorithms for λ-coloring and compute upperbounds of the best possible λ for outerplanar graphs, planar graphs, graphs of treewidth k, permutation and split graphs. With the exception of the split graphs, all the above bounds for λ are linear in Δ, the maximum degree of the graph. For split graphs, we give a bound of λ ≤ Δ1.5+2Δ+2 and show that there are split graphs with λ = Ω(Δ1.5). Similar results are also given for variations of the λ-coloring problem. |
| doi_str_mv | 10.1007/3-540-46541-3_33 |
| format | Book Chapter |
| fullrecord | <record><control><sourceid>proquest_pasca</sourceid><recordid>TN_cdi_pascalfrancis_primary_1177376</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>EBC6414110_300_409</sourcerecordid><originalsourceid>FETCH-LOGICAL-c360t-2db8d1ad0bf2d7b799901de075ab23268362eafd1bf87def38b527d8cb4a51373</originalsourceid><addsrcrecordid>eNqNkM9OwzAMxsNfbRo7InHkwLXDrtO4OaIJBtIkLnCO0jZlg7KWpBx4Nt6BZyLdJs74Yumzf5_sT4gLhBkC8DUlmYREqkxiQoboQEw15xTFraYOxRgVxhlJffQ3U4wS8ViMgSBNNEs6FSOZZZwrySMxDeEVYhECahyL85_vZN42rV9vXi7b-nLhbbcKZ-Kktk1w032fiOe726f5fbJ8XDzMb5ZJSQr6JK2KvEJbQVGnFRestQasHHBmi5RSlZNKna0rLOqcK1dTXmQpV3lZSJshMU3E1c63s6G0Te3tplwH0_n1u_VfBpGZWMW12W4tdMOdzpuibd-CQTBDUoZMfNxsUzFDUhGQe1_ffny60Bs3EKXb9N425cp2vfPBKDlkBYYg0qD_ixEoVMwm1TpiOf0Ce-J2cg</addsrcrecordid><sourcetype>Index Database</sourcetype><iscdi>true</iscdi><recordtype>book_chapter</recordtype><pqid>EBC3061677_299_408</pqid></control><display><type>book_chapter</type><title>λ-Coloring of Graphs</title><source>Springer Books</source><creator>Bodlaender, Hans L. ; Kloks, Ton ; Tan, Richard B. ; van Leeuwen, Jan</creator><contributor>Reichel, Horst ; Tison, Sophie ; Reichel, Horst ; Tison, Sophie</contributor><creatorcontrib>Bodlaender, Hans L. ; Kloks, Ton ; Tan, Richard B. ; van Leeuwen, Jan ; Reichel, Horst ; Tison, Sophie ; Reichel, Horst ; Tison, Sophie</creatorcontrib><description>A λ-coloring of a graph G is an assignment of colors from the set 0, ..., λ to the vertices of a graph G such that vertices at distance at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-colorings with small or optimal λ arises in the context of radio frequency assignment. We show that the problems of finding the minimum λ for planar graphs, bipartite graphs, chordal graphs and split graphs are NP-Complete. We then give approximation algorithms for λ-coloring and compute upperbounds of the best possible λ for outerplanar graphs, planar graphs, graphs of treewidth k, permutation and split graphs. With the exception of the split graphs, all the above bounds for λ are linear in Δ, the maximum degree of the graph. For split graphs, we give a bound of λ ≤ Δ1.5+2Δ+2 and show that there are split graphs with λ = Ω(Δ1.5). Similar results are also given for variations of the λ-coloring problem.</description><identifier>ISSN: 0302-9743</identifier><identifier>ISBN: 9783540671411</identifier><identifier>ISBN: 3540671412</identifier><identifier>EISSN: 1611-3349</identifier><identifier>EISBN: 9783540465416</identifier><identifier>EISBN: 3540465413</identifier><identifier>DOI: 10.1007/3-540-46541-3_33</identifier><identifier>OCLC: 45578647</identifier><identifier>LCCallNum: QA75.5 -- .S956 2000eb</identifier><language>eng</language><publisher>Germany: Springer Berlin / Heidelberg</publisher><subject>Applied sciences ; Bipartite Graph ; Computer science; control theory; systems ; Exact sciences and technology ; Information retrieval. Graph ; Interval Graph ; Planar Graph ; Polynomial Time Algorithm ; Theoretical computing ; Tree Decomposition</subject><ispartof>Lecture notes in computer science, 2000, Vol.1770, p.395-406</ispartof><rights>Springer-Verlag Berlin Heidelberg 2000</rights><rights>2000 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c360t-2db8d1ad0bf2d7b799901de075ab23268362eafd1bf87def38b527d8cb4a51373</citedby><relation>Lecture Notes in Computer Science</relation></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Uhttps://ebookcentral.proquest.com/covers/3061677-l.jpg</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/3-540-46541-3_33$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/3-540-46541-3_33$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>309,310,775,776,780,785,786,789,27902,38232,41418,42487</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=1177376$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><contributor>Reichel, Horst</contributor><contributor>Tison, Sophie</contributor><contributor>Reichel, Horst</contributor><contributor>Tison, Sophie</contributor><creatorcontrib>Bodlaender, Hans L.</creatorcontrib><creatorcontrib>Kloks, Ton</creatorcontrib><creatorcontrib>Tan, Richard B.</creatorcontrib><creatorcontrib>van Leeuwen, Jan</creatorcontrib><title>λ-Coloring of Graphs</title><title>Lecture notes in computer science</title><description>A λ-coloring of a graph G is an assignment of colors from the set 0, ..., λ to the vertices of a graph G such that vertices at distance at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-colorings with small or optimal λ arises in the context of radio frequency assignment. We show that the problems of finding the minimum λ for planar graphs, bipartite graphs, chordal graphs and split graphs are NP-Complete. We then give approximation algorithms for λ-coloring and compute upperbounds of the best possible λ for outerplanar graphs, planar graphs, graphs of treewidth k, permutation and split graphs. With the exception of the split graphs, all the above bounds for λ are linear in Δ, the maximum degree of the graph. For split graphs, we give a bound of λ ≤ Δ1.5+2Δ+2 and show that there are split graphs with λ = Ω(Δ1.5). Similar results are also given for variations of the λ-coloring problem.</description><subject>Applied sciences</subject><subject>Bipartite Graph</subject><subject>Computer science; control theory; systems</subject><subject>Exact sciences and technology</subject><subject>Information retrieval. Graph</subject><subject>Interval Graph</subject><subject>Planar Graph</subject><subject>Polynomial Time Algorithm</subject><subject>Theoretical computing</subject><subject>Tree Decomposition</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>9783540671411</isbn><isbn>3540671412</isbn><isbn>9783540465416</isbn><isbn>3540465413</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>2000</creationdate><recordtype>book_chapter</recordtype><recordid>eNqNkM9OwzAMxsNfbRo7InHkwLXDrtO4OaIJBtIkLnCO0jZlg7KWpBx4Nt6BZyLdJs74Yumzf5_sT4gLhBkC8DUlmYREqkxiQoboQEw15xTFraYOxRgVxhlJffQ3U4wS8ViMgSBNNEs6FSOZZZwrySMxDeEVYhECahyL85_vZN42rV9vXi7b-nLhbbcKZ-Kktk1w032fiOe726f5fbJ8XDzMb5ZJSQr6JK2KvEJbQVGnFRestQasHHBmi5RSlZNKna0rLOqcK1dTXmQpV3lZSJshMU3E1c63s6G0Te3tplwH0_n1u_VfBpGZWMW12W4tdMOdzpuibd-CQTBDUoZMfNxsUzFDUhGQe1_ffny60Bs3EKXb9N425cp2vfPBKDlkBYYg0qD_ixEoVMwm1TpiOf0Ce-J2cg</recordid><startdate>20000101</startdate><enddate>20000101</enddate><creator>Bodlaender, Hans L.</creator><creator>Kloks, Ton</creator><creator>Tan, Richard B.</creator><creator>van Leeuwen, Jan</creator><general>Springer Berlin / Heidelberg</general><general>Springer Berlin Heidelberg</general><general>Springer</general><scope>FFUUA</scope><scope>IQODW</scope></search><sort><creationdate>20000101</creationdate><title>λ-Coloring of Graphs</title><author>Bodlaender, Hans L. ; Kloks, Ton ; Tan, Richard B. ; van Leeuwen, Jan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c360t-2db8d1ad0bf2d7b799901de075ab23268362eafd1bf87def38b527d8cb4a51373</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>2000</creationdate><topic>Applied sciences</topic><topic>Bipartite Graph</topic><topic>Computer science; control theory; systems</topic><topic>Exact sciences and technology</topic><topic>Information retrieval. Graph</topic><topic>Interval Graph</topic><topic>Planar Graph</topic><topic>Polynomial Time Algorithm</topic><topic>Theoretical computing</topic><topic>Tree Decomposition</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bodlaender, Hans L.</creatorcontrib><creatorcontrib>Kloks, Ton</creatorcontrib><creatorcontrib>Tan, Richard B.</creatorcontrib><creatorcontrib>van Leeuwen, Jan</creatorcontrib><collection>ProQuest Ebook Central - Book Chapters - Demo use only</collection><collection>Pascal-Francis</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bodlaender, Hans L.</au><au>Kloks, Ton</au><au>Tan, Richard B.</au><au>van Leeuwen, Jan</au><au>Reichel, Horst</au><au>Tison, Sophie</au><au>Reichel, Horst</au><au>Tison, Sophie</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>λ-Coloring of Graphs</atitle><btitle>Lecture notes in computer science</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>2000-01-01</date><risdate>2000</risdate><volume>1770</volume><spage>395</spage><epage>406</epage><pages>395-406</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>9783540671411</isbn><isbn>3540671412</isbn><eisbn>9783540465416</eisbn><eisbn>3540465413</eisbn><abstract>A λ-coloring of a graph G is an assignment of colors from the set 0, ..., λ to the vertices of a graph G such that vertices at distance at most two get different colors and adjacent vertices get colors which are at least two apart. The problem of finding λ-colorings with small or optimal λ arises in the context of radio frequency assignment. We show that the problems of finding the minimum λ for planar graphs, bipartite graphs, chordal graphs and split graphs are NP-Complete. We then give approximation algorithms for λ-coloring and compute upperbounds of the best possible λ for outerplanar graphs, planar graphs, graphs of treewidth k, permutation and split graphs. With the exception of the split graphs, all the above bounds for λ are linear in Δ, the maximum degree of the graph. For split graphs, we give a bound of λ ≤ Δ1.5+2Δ+2 and show that there are split graphs with λ = Ω(Δ1.5). Similar results are also given for variations of the λ-coloring problem.</abstract><cop>Germany</cop><pub>Springer Berlin / Heidelberg</pub><doi>10.1007/3-540-46541-3_33</doi><oclcid>45578647</oclcid><tpages>12</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Lecture notes in computer science, 2000, Vol.1770, p.395-406 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_pascalfrancis_primary_1177376 |
| source | Springer Books |
| subjects | Applied sciences Bipartite Graph Computer science control theory systems Exact sciences and technology Information retrieval. Graph Interval Graph Planar Graph Polynomial Time Algorithm Theoretical computing Tree Decomposition |
| title | λ-Coloring of Graphs |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-29T01%3A49%3A51IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_pasca&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=bookitem&rft.atitle=%CE%BB-Coloring%20of%20Graphs&rft.btitle=Lecture%20notes%20in%20computer%20science&rft.au=Bodlaender,%20Hans%20L.&rft.date=2000-01-01&rft.volume=1770&rft.spage=395&rft.epage=406&rft.pages=395-406&rft.issn=0302-9743&rft.eissn=1611-3349&rft.isbn=9783540671411&rft.isbn_list=3540671412&rft_id=info:doi/10.1007/3-540-46541-3_33&rft_dat=%3Cproquest_pasca%3EEBC6414110_300_409%3C/proquest_pasca%3E%3Curl%3E%3C/url%3E&rft.eisbn=9783540465416&rft.eisbn_list=3540465413&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=EBC3061677_299_408&rft_id=info:pmid/&rfr_iscdi=true |