{"id":"https://openalex.org/W2027828847","doi":"https://doi.org/10.1137/070691486","title":"Multiple Coloring of Cone Graphs","display_name":"Multiple Coloring of Cone Graphs","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2027828847","doi":"https://doi.org/10.1137/070691486","mag":"2027828847"},"language":"en","primary_location":{"id":"doi:10.1137/070691486","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070691486","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014539914","display_name":"Zhishi Pan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhishi Pan","raw_affiliation_strings":["zhishi@mail.tku.edu.tw#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"zhishi@mail.tku.edu.tw#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020969478","display_name":"Xuding Zhu","orcid":"https://orcid.org/0000-0002-5502-5390"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xuding Zhu","raw_affiliation_strings":["xudingzhu@gmail.com#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"xudingzhu@gmail.com#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4693,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.59203445,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"24","issue":"4","first_page":"1515","last_page":"1526"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9842000007629395,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.928421676158905},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8019541501998901},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6026013493537903},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.587310791015625},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5524592995643616},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5244281888008118},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.44628095626831055},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4040069878101349},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.21653932332992554},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.08396753668785095}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.928421676158905},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8019541501998901},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6026013493537903},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.587310791015625},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5524592995643616},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5244281888008118},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.44628095626831055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4040069878101349},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.21653932332992554},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.08396753668785095}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070691486","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070691486","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:tkuir.lib.tku.edu.tw:987654321/56752","is_oa":false,"landing_page_url":"https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/56752","pdf_url":null,"source":{"id":"https://openalex.org/S4406922698","display_name":"Tamkang University Institutional Repository (TKUIR)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W617577063","https://openalex.org/W1526979981","https://openalex.org/W1529283357","https://openalex.org/W1540614089","https://openalex.org/W1572041907","https://openalex.org/W1963931974","https://openalex.org/W1984640610","https://openalex.org/W1985826196","https://openalex.org/W2003995429","https://openalex.org/W2012032721","https://openalex.org/W2015307128","https://openalex.org/W2019885050","https://openalex.org/W2056289686","https://openalex.org/W2069232717","https://openalex.org/W2098751286","https://openalex.org/W2130738665","https://openalex.org/W2170803232","https://openalex.org/W2599950914","https://openalex.org/W4244881898"],"related_works":["https://openalex.org/W1971174658","https://openalex.org/W2099195351","https://openalex.org/W4256429076","https://openalex.org/W2012063272","https://openalex.org/W2348092930","https://openalex.org/W2062850566","https://openalex.org/W4308716484","https://openalex.org/W2098284475","https://openalex.org/W2950817880","https://openalex.org/W3178681420"],"abstract_inverted_index":{"A":[0],"k-fold":[1,43],"coloring":[2,44],"of":[3,12,29,38,45,57,74,98,109,141,145,152],"a":[4,10,30,42,48,133],"graph":[5,31,49,124,144],"assigns":[6],"to":[7,19,71],"each":[8],"vertex":[9,63,73],"set":[11,64],"k":[13],"colors,":[14],"and":[15,51,76,84,89,112,147,160,174],"color":[16],"sets":[17],"assigned":[18],"adjacent":[20,70],"vertices":[21],"are":[22,114],"disjoint.":[23],"The":[24],"kth":[25,95,138],"chromatic":[26,96,139,150],"number":[27,37,97,140,151],"$\\chi_k(G)$":[28,161],"G":[32,146],"is":[33,69,78,119,155,162,176],"the":[34,55,94,99,137,142,148],"minimum":[35],"total":[36],"colors":[39],"needed":[40],"in":[41,66,107],"G.":[46,153],"Given":[47],"$G=(V,E)$":[50],"an":[52,79],"integer":[53],"$m\\geq0$,":[54],"m-cone":[56],"G,":[58,125],"denoted":[59],"by":[60],"$\\mu_m(G)$,":[61],"has":[62],"$(V\\times\\{0,1,\\dots,m\\})\\cup\\{u\\}$":[65],"which":[67],"u":[68],"every":[72],"$V\\times\\{m\\}$,":[75],"$(x,i)(y,j)$":[77],"edge":[80],"if":[81,126,158,172],"$xy\\in":[82,87],"E$":[83,88],"$i=j=0$":[85],"or":[86],"$|i-j|=1$.":[90],"This":[91],"paper":[92],"studies":[93],"cone":[100,143],"graphs.":[101],"An":[102],"upper":[103],"bound":[104],"for":[105,122,165,179],"$\\chi_k(\\mu_m(G))$":[106],"terms":[108],"$\\chi_k(G)$,":[110],"k,":[111],"m":[113],"given.":[115],"In":[116,170],"particular,":[117,171],"it":[118],"proved":[120,156],"that":[121,157],"any":[123],"$m\\geq2k$,":[127],"then":[128,164,178],"$\\chi_k(\\mu_m(G))\\leq\\chi_k(G)+1$.":[129],"We":[130],"also":[131],"find":[132],"surprising":[134],"connection":[135],"between":[136],"circular":[149],"It":[154],"$\\chi_k(G)/k>\\chi_c(G)$":[159],"even,":[163,177],"sufficiently":[166,180],"large":[167,181],"m,":[168,182],"$\\chi_k(\\mu_m(G))=\\chi_k(G)$.":[169],"$\\chi(G)>\\chi_c(G)$":[173],"$\\chi(G)$":[175],"$\\chi(\\mu_m(G))=\\chi(G)$.":[183]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
