{"id":"https://openalex.org/W2129907634","doi":"https://doi.org/10.1145/1132516.1132576","title":"Approximating the list-chromatic number and the chromatic number in minor-closed and odd-minor-closed classes of graphs","display_name":"Approximating the list-chromatic number and the chromatic number in minor-closed and odd-minor-closed classes of graphs","publication_year":2006,"publication_date":"2006-05-21","ids":{"openalex":"https://openalex.org/W2129907634","doi":"https://doi.org/10.1145/1132516.1132576","mag":"2129907634"},"language":"en","primary_location":{"id":"doi:10.1145/1132516.1132576","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1132516.1132576","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-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/A5008961593","display_name":"Ken\u2010ichi Kawarabayashi","orcid":"https://orcid.org/0000-0001-6056-4287"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Ken-ichi Kawarabayashi","raw_affiliation_strings":["Tohoku University, Sendai, Japan","Tohoku University Sendai, Japan#TAB#"],"affiliations":[{"raw_affiliation_string":"Tohoku University, Sendai, Japan","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Tohoku University Sendai, Japan#TAB#","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005993212","display_name":"Bojan Mohar","orcid":"https://orcid.org/0000-0002-7408-6148"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Bojan Mohar","raw_affiliation_strings":["University of Ljubljana, Ljubljana, Slovenia","University of Ljubljana; Ljubljana; Slovenia"],"affiliations":[{"raw_affiliation_string":"University of Ljubljana, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]},{"raw_affiliation_string":"University of Ljubljana; Ljubljana; Slovenia","institution_ids":["https://openalex.org/I153976015"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5008961593"],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":null,"apc_paid":null,"fwci":3.3703,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.92465178,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"401","last_page":"416"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998000264167786,"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":0.9998000264167786,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9965000152587891,"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":0.8411954045295715},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.7223120331764221},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6368519067764282},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.5594860911369324},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47527092695236206},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.46729663014411926},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.46703028678894043},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.44577527046203613},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.29301750659942627}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8411954045295715},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.7223120331764221},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6368519067764282},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.5594860911369324},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47527092695236206},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.46729663014411926},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.46703028678894043},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.44577527046203613},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.29301750659942627},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/1132516.1132576","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1132516.1132576","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.103.4688","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.4688","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ijp.si/ftp/pub/preprints/ps/2006/pp1007.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.418.665","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.418.665","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.imfm.si/preprinti/PDF/01007.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.626.1895","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.626.1895","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.sfu.ca/~mohar/Reprints/2006/BM06_38STC_Kawarabayashi_MinorClosedGraphs.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":76,"referenced_works":["https://openalex.org/W10105891","https://openalex.org/W48861618","https://openalex.org/W136000211","https://openalex.org/W345637930","https://openalex.org/W574460519","https://openalex.org/W1481873605","https://openalex.org/W1484819834","https://openalex.org/W1489979173","https://openalex.org/W1496725729","https://openalex.org/W1507311961","https://openalex.org/W1520619927","https://openalex.org/W1529433769","https://openalex.org/W1535899844","https://openalex.org/W1566410171","https://openalex.org/W1656795039","https://openalex.org/W1965380924","https://openalex.org/W1965737603","https://openalex.org/W1967516408","https://openalex.org/W1969919767","https://openalex.org/W1975659026","https://openalex.org/W1977080610","https://openalex.org/W1979506099","https://openalex.org/W1981295749","https://openalex.org/W1984537627","https://openalex.org/W1987092466","https://openalex.org/W1989544707","https://openalex.org/W1991755800","https://openalex.org/W1996858528","https://openalex.org/W2004102446","https://openalex.org/W2005079828","https://openalex.org/W2012329067","https://openalex.org/W2013664277","https://openalex.org/W2019624146","https://openalex.org/W2019992365","https://openalex.org/W2020819035","https://openalex.org/W2027399467","https://openalex.org/W2032684479","https://openalex.org/W2035409201","https://openalex.org/W2042899161","https://openalex.org/W2046693802","https://openalex.org/W2047993669","https://openalex.org/W2054040057","https://openalex.org/W2055443873","https://openalex.org/W2058422149","https://openalex.org/W2059021689","https://openalex.org/W2059372025","https://openalex.org/W2068706708","https://openalex.org/W2071321409","https://openalex.org/W2081254453","https://openalex.org/W2082001376","https://openalex.org/W2089023036","https://openalex.org/W2089726838","https://openalex.org/W2094667324","https://openalex.org/W2122076180","https://openalex.org/W2125690626","https://openalex.org/W2130481157","https://openalex.org/W2131433460","https://openalex.org/W2132877659","https://openalex.org/W2135517930","https://openalex.org/W2148360835","https://openalex.org/W2151438396","https://openalex.org/W2154119795","https://openalex.org/W2156678756","https://openalex.org/W2166232733","https://openalex.org/W2170662028","https://openalex.org/W2170758948","https://openalex.org/W2313828007","https://openalex.org/W2336629689","https://openalex.org/W2427045451","https://openalex.org/W3000633136","https://openalex.org/W3140862644","https://openalex.org/W4212970601","https://openalex.org/W4389615578","https://openalex.org/W4389615663","https://openalex.org/W6605521613","https://openalex.org/W6611624771"],"related_works":["https://openalex.org/W2467936747","https://openalex.org/W2368619281","https://openalex.org/W2377143628","https://openalex.org/W2355995962","https://openalex.org/W2392462513","https://openalex.org/W2362718971","https://openalex.org/W2368173763","https://openalex.org/W2977970519","https://openalex.org/W191560551","https://openalex.org/W2950817880"],"abstract_inverted_index":{"It":[0,43],"is":[1,35,44,55,61,105,121,138,278,325,332,351,440],"well-known":[2,310,413],"(Feige":[3],"and":[4,70,87,119,140,150,154,165,203,379,418,511],"Kilian":[5],"[24],":[6],"H\u00e5stad":[7],"[39])":[8],"that":[9,46,103,173,193,217,235,290,359,456,483],"approximating":[10],"the":[11,32,40,47,52,112,128,155,207,218,221,226,236,250,305,309,348,387,392,412,512,523],"chromatic":[12,41,129,166],"number":[13,34,54,114,130,164,167],"within":[14,220],"a":[15,93,106,122,215,242,283,352,361,434,444,452,461],"factor":[16],"of":[17,49,73,96,115,131,180,196,209,274,308,375,395,415,437,447,487,500,505,515,520],"n1-\u03b5":[18],"cannot":[19],"be":[20,295],"done":[21],"in":[22,190,204,213,327],"polynomial":[23,107,123],"time":[24,108,124,136],"for":[25,92,111,127,160,244,260,347,368,386,470],"\u03b5>0,":[26],"unless":[27],"coRP":[28],"=":[29],"NP.":[30],"Computing":[31],"list-chromatic":[33,53,113,163],"much":[36],"harder":[37],"than":[38],"determining":[39],"number.":[42],"known":[45,345],"problem":[48],"deciding":[50,471],"if":[51,183],"k,":[56,97],"where":[57],"k":[58,245,262],"\u2265":[59,263],"3,":[60],"\u03a02p-complete":[62],"[37].In":[63],"this":[64,484,494],"paper,":[65],"we":[66,78,424,450,464],"focus":[67],"on":[68,249,335,339],"minor-closed":[69,503],"odd-minor-closed":[71,518],"families":[72],"graphs.":[74,370],"In":[75,422],"doing":[76],"that,":[77],"may":[79],"as":[80,297],"well":[81],"consider":[82],"only":[83,159],"graphs":[84,88,116,132,161,267,341,506,521],"without":[85,89,117,133],"Kk-minors":[86,91,118],"odd":[90,177,258,306,420],"fixed":[94],"value":[95],"respectively.":[98,142],"Our":[99],"main":[100,318],"results":[101,374,501,516],"are":[102,168,185,198,211,223,230,268,491],"there":[104,120,184],"approximation":[109,125,346,385],"algorithm":[110,126,358,410,428,469],"odd-Kk-minors.":[134],"Their":[135],"complexity":[137],"O(n3)":[139,427],"O(n4),":[141],"The":[143,496],"algorithms":[144],"have":[145],"multiplicative":[146,156],"error":[147,152,157],"O(\u221alog":[148],"k)":[149,366],"additive":[151],"O(k),":[153],"occurs":[158],"whose":[162],"\u0398(k),":[169],"respectively.Let":[170],"us":[171,233,481],"recall":[172],"H":[174,191],"has":[175,286,313],"an":[176,201,257,402,426,467,479],"complete":[178,237],"minor":[179],"order":[181],"l":[182,186],"vertex":[187],"disjoint":[188],"trees":[189,210,222,229],"such":[192,214],"every":[194],"two":[195,488,508],"them":[197],"joined":[199],"by":[200,443,507,522],"edge,":[202],"addition,":[205],"all":[206],"vertices":[208],"two-colored":[212],"way":[216],"edges":[219,227],"bichromatic,":[224],"but":[225,248],"between":[228],"monochromatic.":[231],"Let":[232],"observe":[234],"bipartite":[238],"graph":[239,459,477],"Kn/2,n/2":[240],"contains":[241,460,478],"Kk-minor":[243,259],"\u2264":[246],"n/2,":[247],"other":[251,513],"hand,":[252],"it":[253],"does":[254],"not":[255,433,474],"contain":[256],"any":[261,457,475],"3.":[264],"Odd":[265],"K5-minor-free":[266],"closely":[269],"related":[270],"to":[271,411,429],"one":[272,330,498],"field":[273],"discrete":[275],"optimization":[276,292],"which":[277,282,454,490],"finding":[279],"conditions":[280],"under":[281],"given":[284],"polyhedron":[285],"integer":[287,291],"vertices,":[288],"so":[289],"problems":[293],"can":[294],"solved":[296],"linear":[298],"programs.":[299],"See":[300],"[33,":[301],"34,":[302],"64].":[303],"Also,":[304,463],"version":[307,436,446],"Hadwiger's":[311,438,448],"conjecture":[312,414,439,453],"been":[314],"considered,":[315],"see":[316],"[28].Our":[317],"idea":[319,324],"involves":[320],"precoloring":[321],"extension.":[322],"This":[323,371],"used":[326],"many":[328],"results;":[329],"example":[331],"Thomassen's":[333],"proof":[334],"his":[336],"celebrated":[337],"theorem":[338],"planar":[340],"[69].The":[342],"best":[343,383],"previously":[344],"first":[349,497,524],"result":[350,389,394],"simple":[353],"O(k":[354,364,403],"\u221alog":[355,365,404],"k)-approximation":[356,405],"following":[357],"guarantees":[360],"list-coloring":[362],"with":[363],"colors":[367],"Kk-minor-free":[369],"follows":[372],"from":[373,391],"Kostochka":[376],"[54,":[377],"53]":[378],"Thomason":[380],"[67,":[381],"68].The":[382],"previous":[384],"second":[388],"comes":[390],"recent":[393],"Geelen":[396],"et":[397],"al.":[398],"[28]":[399],"who":[400],"gave":[401],"algorithm.We":[406],"also":[407],"relate":[408],"our":[409],"Hadwiger":[416],"[38]":[417],"its":[419],"version.":[421],"fact,":[423],"give":[425,466],"decide":[430],"whether":[431,472],"or":[432,473],"weaker":[435,445],"true.":[441],"Here,":[442],"conjecture,":[449],"mean":[451],"says":[455],"27k-chromatic":[458],"Kk-minor.":[462],"shall":[465],"O(n2500k)":[468],"2500k-chromatic":[476],"odd-Kk-minor.Let":[480],"mention":[482],"presentation":[485],"consists":[486,499,514],"papers":[489],"merged":[492],"into":[493],"one.":[495],"concerning":[502,517],"classes":[504,519],"current":[509],"authors,":[510],"author.":[525]},"counts_by_year":[{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
