{"id":"https://openalex.org/W7161744254","doi":"https://doi.org/10.48550/arxiv.2605.18634","title":"Harmonious Colorings: bounds, heuristics and integer-linear formulations","display_name":"Harmonious Colorings: bounds, heuristics and integer-linear formulations","publication_year":2026,"publication_date":"2026-05-18","ids":{"openalex":"https://openalex.org/W7161744254","doi":"https://doi.org/10.48550/arxiv.2605.18634"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.18634","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.18634","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.18634","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136454896","display_name":"J\u00falio Ara\u00fajo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ara\u00fajo, J\u00falio","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001592356","display_name":"Manoel Camp\u00ealo","orcid":"https://orcid.org/0000-0003-2962-2033"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Camp\u00ealo, Manoel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136499997","display_name":"Beatriz Martins","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Martins, Beatriz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5038718843","display_name":"M\u00e1rcio C. Santos","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Santos, Marcio C.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.5580000281333923,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12401","display_name":"Scheduling and Timetabling Solutions","score":0.5580000281333923,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.1395999938249588,"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":0.09740000218153,"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/parameterized-complexity","display_name":"Parameterized complexity","score":0.7135999798774719},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.635200023651123},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5317000150680542},{"id":"https://openalex.org/keywords/graph-coloring","display_name":"Graph coloring","score":0.46470001339912415},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4408000111579895},{"id":"https://openalex.org/keywords/integer-programming","display_name":"Integer programming","score":0.43689998984336853},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.43549999594688416}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7135999798774719},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.635200023651123},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6229000091552734},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5317000150680542},{"id":"https://openalex.org/C76946457","wikidata":"https://www.wikidata.org/wiki/Q504843","display_name":"Graph coloring","level":3,"score":0.46470001339912415},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4408000111579895},{"id":"https://openalex.org/C56086750","wikidata":"https://www.wikidata.org/wiki/Q6042592","display_name":"Integer programming","level":2,"score":0.43689998984336853},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.43549999594688416},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4334999918937683},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41119998693466187},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3935000002384186},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.3700999915599823},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.3463999927043915},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32199999690055847},{"id":"https://openalex.org/C51658606","wikidata":"https://www.wikidata.org/wiki/Q512897","display_name":"Brooks' theorem","level":5,"score":0.3167000114917755},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.30079999566078186},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.29980000853538513},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2921999990940094},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2732999920845032},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C158319403","wikidata":"https://www.wikidata.org/wiki/Q5477527","display_name":"Fractional coloring","level":5,"score":0.25540000200271606},{"id":"https://openalex.org/C167750561","wikidata":"https://www.wikidata.org/wiki/Q1789512","display_name":"Critical graph","level":5,"score":0.25200000405311584}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.18634","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.18634","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.18634","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.18634","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"proper":[1],"coloring":[2,46],"$c$":[3],"of":[4,15,29,81,116,130],"a":[5,44,104],"simple":[6],"graph":[7],"$G$":[8,42,84,92],"is":[9,34],"harmonious":[10,26,45,78],"if,":[11],"for":[12,136],"every":[13],"pair":[14],"distinct":[16],"edges":[17],"$uv,xy\\in":[18],"E(G)$,":[19],"we":[20,53,111],"have":[21],"that":[22,41],"$\\{c(u),c(v)\\}\\neq":[23],"\\{c(x),c(y)\\}$.":[24],"The":[25],"chromatic":[27,79],"number":[28],"$G$,":[30],"denoted":[31],"by":[32,93,102],"$h(G)$,":[33],"the":[35,77,108,125,128,140,157],"least":[36,99],"positive":[37],"integer":[38],"$k$":[39,48],"such":[40],"has":[43],"with":[47,87,143],"colors.":[49],"In":[50],"this":[51,137],"work,":[52,110],"extend":[54],"an":[55],"idea":[56],"presented":[57,106],"in":[58,107,139],"[Kolay,":[59],"et":[60],"al.":[61],"Harmonious":[62],"coloring:":[63],"Parameterized":[64],"algorithms":[65],"and":[66,85,123,154],"upper":[67,118],"bounds.":[68,119],"Theor.":[69],"Comp.":[70],"Sci.":[71],"772":[72],"(2019),":[73],"132-142]":[74],"to":[75,113,127],"compare":[76],"numbers":[80],"two":[82],"graphs":[83],"$H$,":[86],"$H$":[88],"being":[89],"obtained":[90],"from":[91,156],"identifying":[94],"vertices":[95],"at":[96,98],"distance":[97],"three.":[100],"Furthermore,":[101],"fixing":[103],"proof":[105],"same":[109],"manage":[112],"improve":[114],"one":[115],"its":[117],"We":[120,146],"also":[121],"introduce":[122],"study":[124],"first,":[126],"best":[129],"our":[131],"knowledge,":[132],"integer-linear":[133],"programming":[134],"formulations":[135],"problem":[138],"literature,":[141],"along":[142],"some":[144,148],"heuristics.":[145],"provide":[147],"preliminary":[149],"tests":[150],"on":[151],"random":[152],"instances":[153,155],"second":[158],"DIMACS":[159],"Implementation":[160],"Challenge.":[161]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-20T00:00:00"}
