{"id":"https://openalex.org/W2247104300","doi":"https://doi.org/10.37236/5390","title":"On the Strong Chromatic Index of Sparse Graphs","display_name":"On the Strong Chromatic Index of Sparse Graphs","publication_year":2018,"publication_date":"2018-07-27","ids":{"openalex":"https://openalex.org/W2247104300","doi":"https://doi.org/10.37236/5390","mag":"2247104300"},"language":"en","primary_location":{"id":"doi:10.37236/5390","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5390","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/5390","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048689775","display_name":"Philip DeOrsey","orcid":null},"institutions":[{"id":"https://openalex.org/I46506128","display_name":"Westfield State University","ror":"https://ror.org/05pjd6b26","country_code":"US","type":"education","lineage":["https://openalex.org/I46506128"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Philip DeOrsey","raw_affiliation_strings":["Westfield State University"],"affiliations":[{"raw_affiliation_string":"Westfield State University","institution_ids":["https://openalex.org/I46506128"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101939674","display_name":"Michael Ferrara","orcid":"https://orcid.org/0000-0001-7369-8751"},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Ferrara","raw_affiliation_strings":["University of Colorado Denver"],"affiliations":[{"raw_affiliation_string":"University of Colorado Denver","institution_ids":["https://openalex.org/I921990950"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045183927","display_name":"Nathan Graber","orcid":null},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nathan Graber","raw_affiliation_strings":["University of Colorado Denver"],"affiliations":[{"raw_affiliation_string":"University of Colorado Denver","institution_ids":["https://openalex.org/I921990950"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070304707","display_name":"Stephen G. Hartke","orcid":"https://orcid.org/0000-0003-1278-0860"},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Stephen G. Hartke","raw_affiliation_strings":["University of Colorado Denver"],"affiliations":[{"raw_affiliation_string":"University of Colorado Denver","institution_ids":["https://openalex.org/I921990950"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066588212","display_name":"Luke L. Nelsen","orcid":"https://orcid.org/0000-0003-1310-5621"},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luke L. Nelsen","raw_affiliation_strings":["University of Colorado Denver"],"affiliations":[{"raw_affiliation_string":"University of Colorado Denver","institution_ids":["https://openalex.org/I921990950"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030994635","display_name":"Eric Sullivan","orcid":null},"institutions":[{"id":"https://openalex.org/I921990950","display_name":"University of Colorado Denver","ror":"https://ror.org/02hh7en24","country_code":"US","type":"education","lineage":["https://openalex.org/I921990950"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Eric Sullivan","raw_affiliation_strings":["University of Colorado Denver"],"affiliations":[{"raw_affiliation_string":"University of Colorado Denver","institution_ids":["https://openalex.org/I921990950"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081589836","display_name":"Sogol Jahanbekam","orcid":"https://orcid.org/0000-0003-0948-5713"},"institutions":[{"id":"https://openalex.org/I155173764","display_name":"Rochester Institute of Technology","ror":"https://ror.org/00v4yb702","country_code":"US","type":"education","lineage":["https://openalex.org/I155173764"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sogol Jahanbekam","raw_affiliation_strings":["Rochester Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Rochester Institute of Technology","institution_ids":["https://openalex.org/I155173764"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052932128","display_name":"Bernard Lidick\u00fd","orcid":"https://orcid.org/0000-0001-8612-3594"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bernard Lidick\u00fd","raw_affiliation_strings":["Iowa State University"],"affiliations":[{"raw_affiliation_string":"Iowa State University","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000119939","display_name":"Derrick Stolee","orcid":"https://orcid.org/0000-0002-7165-6520"},"institutions":[{"id":"https://openalex.org/I4210164937","display_name":"Microsoft Research (United Kingdom)","ror":"https://ror.org/05k87vq12","country_code":"GB","type":"company","lineage":["https://openalex.org/I1290206253","https://openalex.org/I4210164937"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Derrick Stolee","raw_affiliation_strings":["Microsoft"],"affiliations":[{"raw_affiliation_string":"Microsoft","institution_ids":["https://openalex.org/I4210164937"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001817427","display_name":"Jennifer White","orcid":null},"institutions":[{"id":"https://openalex.org/I188871143","display_name":"Saint Vincent College","ror":"https://ror.org/00amjd520","country_code":"US","type":"education","lineage":["https://openalex.org/I188871143"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jennifer White","raw_affiliation_strings":["Saint Vincent College"],"affiliations":[{"raw_affiliation_string":"Saint Vincent College","institution_ids":["https://openalex.org/I188871143"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":10,"corresponding_author_ids":["https://openalex.org/A5048689775"],"corresponding_institution_ids":["https://openalex.org/I46506128"],"apc_list":null,"apc_paid":null,"fwci":0.2137,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.50748289,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9991000294685364,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9922000169754028,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8764283061027527},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.8037108182907104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7949261665344238},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.6885952353477478},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.6830194592475891},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5766146183013916},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5307688117027283},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5008010864257812},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.48890939354896545},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41212552785873413},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.22762340307235718},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.15288028120994568},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08750921487808228}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8764283061027527},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.8037108182907104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7949261665344238},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.6885952353477478},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.6830194592475891},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5766146183013916},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5307688117027283},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5008010864257812},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.48890939354896545},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41212552785873413},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.22762340307235718},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.15288028120994568},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08750921487808228},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/5390","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5390","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1508.03515","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.03515","pdf_url":"https://arxiv.org/pdf/1508.03515","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"doi:10.37236/5390","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5390","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1479863711","https://openalex.org/W1652355843","https://openalex.org/W1685169779","https://openalex.org/W1969425709","https://openalex.org/W1974811277","https://openalex.org/W1976677460","https://openalex.org/W1987952056","https://openalex.org/W2004006145","https://openalex.org/W2018699805","https://openalex.org/W2035019112","https://openalex.org/W2048352893","https://openalex.org/W2053777090","https://openalex.org/W2093606884","https://openalex.org/W2101397758","https://openalex.org/W2105531552","https://openalex.org/W2138017804","https://openalex.org/W2154929277","https://openalex.org/W2237219011","https://openalex.org/W2738901344","https://openalex.org/W2911280162"],"related_works":["https://openalex.org/W4294379662","https://openalex.org/W194613981","https://openalex.org/W2964130394","https://openalex.org/W2596309465","https://openalex.org/W1601318884","https://openalex.org/W2745072630","https://openalex.org/W3148277336","https://openalex.org/W1993627687","https://openalex.org/W2358631581","https://openalex.org/W2237219011"],"abstract_inverted_index":{"The":[0,31],"strong":[1,32,114,194],"chromatic":[2,34,116],"index":[3],"of":[4,14,48,105,118,182],"a":[5,89,103,136,150,159,178],"graph":[6,92,139,161],"$G$,":[7],"denoted":[8,36],"$\\chi'_s(G)$,":[9],"is":[10,38,88,135,158],"the":[11,39,75,78,113,153,193],"least":[12,40],"number":[13,117],"colors":[15],"needed":[16],"to":[17,53,83,192],"edge-color":[18],"$G$":[19,57,87,134,157],"so":[20],"that":[21,44,85,132],"edges":[22,65],"at":[23,25,66,68,165],"distance":[24,67],"most":[26,69,166],"two":[27,70],"receive":[28,71],"distinct":[29,72],"colors.":[30],"list":[33],"index,":[35],"$\\chi'_{s,\\ell}(G)$,":[37],"integer":[41],"$k$":[42,50],"such":[43],"if":[45,86,133,156],"arbitrary":[46],"lists":[47,63],"size":[49],"are":[51],"assigned":[52],"each":[54],"edge":[55,115,195],"then":[56,98,145,173],"can":[58],"be":[59],"edge-colored":[60],"from":[61,152,186],"those":[62],"where":[64],"colors.We":[73],"use":[74],"discharging":[76],"method,":[77],"Combinatorial":[79],"Nullstellensatz,":[80],"and":[81,107,140,168,184,189,199],"computation":[82],"show":[84,131],"subcubic":[90,137],"planar":[91,120,138,160],"with":[93,162],"${\\rm":[94,141,169],"girth}(G)":[95,142,170],"\\geq":[96,143,171],"41$":[97],"$\\chi'_{s,\\ell}(G)":[99],"\\leq":[100,147,175],"5$,":[101,148],"answering":[102],"question":[104],"Borodin":[106],"Ivanova":[108],"[Precise":[109],"upper":[110],"bound":[111,151,181],"for":[112],"sparse":[119],"graphs,":[121],"Discuss.":[122],"Math.":[123],"Graph":[124],"Theory,":[125],"33(4),":[126],"(2014)":[127],"759--770].":[128],"We":[129],"further":[130],"30$,":[144],"$\\chi_s'(G)":[146],"improving":[149,177],"same":[154],"paper.Finally,":[155],"maximum":[163],"degree":[164],"four":[167],"28$,":[172],"$\\chi'_s(G)N":[174],"7$,":[176],"more":[179],"general":[180],"Wang":[183],"Zhao":[185],"[Odd":[187],"graphs":[188],"its":[190],"applications":[191],"coloring,":[196],"Applied":[197],"Mathematics":[198],"Computation,":[200],"325":[201],"(2018),":[202],"246-251]":[203],"in":[204],"this":[205],"case.":[206]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
