{"id":"https://openalex.org/W7166809934","doi":"https://doi.org/10.4230/lipics.icalp.2026.53","title":"Hardness and Approximation for Coloring Digraphs","display_name":"Hardness and Approximation for Coloring Digraphs","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7166809934","doi":"https://doi.org/10.4230/lipics.icalp.2026.53"},"language":"en","primary_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26442","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.53","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.53/LIPIcs.ICALP.2026.53.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.53/LIPIcs.ICALP.2026.53.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5016828567","display_name":"Parinya Chalermsook","orcid":"https://orcid.org/0009-0000-2833-0472"},"institutions":[{"id":"https://openalex.org/I91136226","display_name":"University of Sheffield","ror":"https://ror.org/05krs5044","country_code":"GB","type":"education","lineage":["https://openalex.org/I91136226"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Chalermsook, Parinya","raw_affiliation_strings":["University of Sheffield, UK"],"raw_orcid":"https://orcid.org/0009-0000-2833-0472","affiliations":[{"raw_affiliation_string":"University of Sheffield, UK","institution_ids":["https://openalex.org/I91136226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077797162","display_name":"Harmender Gahlawat","orcid":"https://orcid.org/0000-0001-7663-6265"},"institutions":[{"id":"https://openalex.org/I68891433","display_name":"Indian Institute of Technology Delhi","ror":"https://ror.org/049tgcd06","country_code":"IN","type":"education","lineage":["https://openalex.org/I68891433"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Gahlawat, Harmender","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology Delhi, India"],"raw_orcid":"https://orcid.org/0000-0001-7663-6265","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology Delhi, India","institution_ids":["https://openalex.org/I68891433"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050342154","display_name":"Felix Klingelhoefer","orcid":null},"institutions":[{"id":"https://openalex.org/I4210094718","display_name":"Laboratoire des Sciences pour la Conception, l'Optimisation et la Production","ror":"https://ror.org/00rv5x925","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210094718","https://openalex.org/I4210159245","https://openalex.org/I899635006","https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Klingelhoefer, Felix","raw_affiliation_strings":["G-SCOP, Grenoble-INP, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"G-SCOP, Grenoble-INP, France","institution_ids":["https://openalex.org/I4210094718"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056131799","display_name":"Alantha Newman","orcid":"https://orcid.org/0009-0009-7353-7734"},"institutions":[{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Newman, Alantha","raw_affiliation_strings":["CNRS and ENS Lyon, France"],"raw_orcid":"https://orcid.org/0009-0009-7353-7734","affiliations":[{"raw_affiliation_string":"CNRS and ENS Lyon, France","institution_ids":["https://openalex.org/I113428412","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025402743","display_name":"Chaoliang Tang","orcid":null},"institutions":[{"id":"https://openalex.org/I24943067","display_name":"Fudan University","ror":"https://ror.org/013q1eq08","country_code":"CN","type":"education","lineage":["https://openalex.org/I24943067"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tang, Chaoliang","raw_affiliation_strings":["Fudan University, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fudan University, Shanghai, China","institution_ids":["https://openalex.org/I24943067"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.7874077,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.8691999912261963,"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":0.8691999912261963,"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":0.0632999986410141,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.027000000700354576,"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/digraph","display_name":"Digraph","score":0.8791999816894531},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.6747000217437744},{"id":"https://openalex.org/keywords/directed-graph","display_name":"Directed graph","score":0.4948999881744385},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.476500004529953},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4672999978065491},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4332999885082245},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.40959998965263367},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.36800000071525574}],"concepts":[{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.8791999816894531},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7301999926567078},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.6747000217437744},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.671999990940094},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5135999917984009},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.4948999881744385},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.476500004529953},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4672999978065491},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.40959998965263367},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.36800000071525574},{"id":"https://openalex.org/C2984853995","wikidata":"https://www.wikidata.org/wiki/Q1060343","display_name":"Independence number","level":3,"score":0.36649999022483826},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.35420000553131104},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.34880000352859497},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3384999930858612},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.3181000053882599},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.2822999954223633},{"id":"https://openalex.org/C204911207","wikidata":"https://www.wikidata.org/wiki/Q860609","display_name":"Generating function","level":2,"score":0.2752000093460083},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2581000030040741}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:drops-oai.dagstuhl.de:26442","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.53","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.53/LIPIcs.ICALP.2026.53.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},{"id":"doi:10.4230/lipics.icalp.2026.53","is_oa":true,"landing_page_url":"https://doi.org/10.4230/lipics.icalp.2026.53","pdf_url":null,"source":null,"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":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:drops-oai.dagstuhl.de:26442","is_oa":true,"landing_page_url":"https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.53","pdf_url":"https://drops.dagstuhl.de/storage/00lipics/lipics-vol374-icalp2026/LIPIcs.ICALP.2026.53/LIPIcs.ICALP.2026.53.pdf","source":{"id":"https://openalex.org/S4377196569","display_name":"DROPS (Schloss Dagstuhl \u2013 Leibniz Center for Informatics)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2799853480","host_organization_name":"Schloss Dagstuhl \u2013 Leibniz Center for Informatics","host_organization_lineage":["https://openalex.org/I2799853480"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"InProceedings"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7166809934.pdf","grobid_xml":"https://content.openalex.org/works/W7166809934.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0,26],"dichromatic":[1,153],"number":[2,10,28,154,164],"\u03c7(D)":[3,180],"of":[4,33,39,49,97,109,155,161,166],"a":[5,34,95,159],"digraph":[6],"is":[7,30,85],"the":[8,31,152,162,167],"minimum":[9],"k":[11,19],"such":[12],"that":[13,55,78,118,185],"V(D)":[14],"can":[15,120,137],"be":[16],"partitioned":[17],"into":[18],"subsets,":[20],"each":[21],"inducing":[22],"an":[23,46],"acyclic":[24,27,37],"digraph.":[25],"\u03b1(D)":[29],"cardinality":[32],"largest":[35],"induced":[36],"subdigraph":[38],"D.":[40],"We":[41,51,104,114,147,170],"study":[42],"these":[43,193],"problems":[44],"from":[45],"approximation":[47],"point":[48],"view.":[50],"begin":[52,115],"with":[53,116,141,179],"establishing":[54,117],"even":[56,99],"when":[57,100],"restricted":[58,101],"to":[59,87,94,102],"tournaments,":[60],"approximating":[61],"\u03c7":[62,92],"and":[63,91,183,200,204],"\u03b1":[64,90,165],"remain":[65],"as":[66,68,158],"challenging":[67],"their":[69],"undirected":[70],"counterparts":[71],"on":[72,150],"general":[73],"graphs.":[74],"Specifically,":[75],"we":[76,119,136,195],"establish":[77],"for":[79],"every":[80],"\u03b5":[81],">":[82],"0,":[83],"it":[84],"hard":[86],"approximate":[88,107],"both":[89],"up":[93],"factor":[96],"n^{1-\u03b5}":[98],"tournaments.":[103],"next":[105],"consider":[106,171],"coloring":[108],"digraphs":[110,123,140,157,178,184],"in":[111,131,134,144,175],"special":[112,173],"cases.":[113],"color":[121,138],"\ud835\udcc1-dicolorable":[122],"using":[124],"at":[125],"most":[126],"\ud835\udcc1":[127],"\u22c5":[128],"n^{1-1/(\ud835\udcc1)}":[129],"colors":[130,143],"time":[132],"O(n^{2\ud835\udcc1});":[133],"particular,":[135],"2-dicolorable":[139],"2\u221an":[142],"polynomial":[145],"time.":[146],"then":[148],"focus":[149],"bounding":[151],"dense":[156],"function":[160],"independence":[163],"underlying":[168],"graph.":[169],"two":[172],"cases":[174],"this":[176],"regard:":[177],"\u2264":[181],"2":[182],"do":[186],"not":[187],"contain":[188],"any":[189],"directed":[190],"triangle.":[191],"For":[192],"cases,":[194],"present":[196],"algorithms":[197],"which":[198],"generalize":[199],"improve":[201],"existing":[202],"tools":[203],"results.":[205]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-02T00:00:00"}