{"id":"https://openalex.org/W1516933281","doi":"https://doi.org/10.37236/513","title":"More Counterexamples to the Alon-Saks-Seymour and Rank-Coloring Conjectures","display_name":"More Counterexamples to the Alon-Saks-Seymour and Rank-Coloring Conjectures","publication_year":2011,"publication_date":"2011-02-04","ids":{"openalex":"https://openalex.org/W1516933281","doi":"https://doi.org/10.37236/513","mag":"1516933281"},"language":"en","primary_location":{"id":"doi:10.37236/513","is_oa":true,"landing_page_url":"https://doi.org/10.37236/513","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p26/pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p26/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002085058","display_name":"Sebastian M. Cioab\u0103","orcid":"https://orcid.org/0000-0001-9983-0212"},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sebastian M. Cioab\u0103","raw_affiliation_strings":["University of Delaware"],"affiliations":[{"raw_affiliation_string":"University of Delaware","institution_ids":["https://openalex.org/I86501945"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054251227","display_name":"Michael Tait","orcid":"https://orcid.org/0000-0003-3695-6883"},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Tait","raw_affiliation_strings":["University of Delaware"],"affiliations":[{"raw_affiliation_string":"University of Delaware","institution_ids":["https://openalex.org/I86501945"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002085058"],"corresponding_institution_ids":["https://openalex.org/I86501945"],"apc_list":null,"apc_paid":null,"fwci":0.7547,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.65764185,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"18","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11476","display_name":"Graph theory and applications","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9997000098228455,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.9124276638031006},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8553327322006226},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7938406467437744},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.620546817779541},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5607028007507324},{"id":"https://openalex.org/keywords/counterexample","display_name":"Counterexample","score":0.551970899105072},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5074700713157654},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4738334119319916},{"id":"https://openalex.org/keywords/list-coloring","display_name":"List coloring","score":0.4508322775363922},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.44732141494750977},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3525652289390564},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34547436237335205},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.12825235724449158},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.058167964220047}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9124276638031006},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8553327322006226},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7938406467437744},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.620546817779541},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5607028007507324},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.551970899105072},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5074700713157654},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4738334119319916},{"id":"https://openalex.org/C199594403","wikidata":"https://www.wikidata.org/wiki/Q1130404","display_name":"List coloring","level":5,"score":0.4508322775363922},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.44732141494750977},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3525652289390564},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34547436237335205},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.12825235724449158},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.058167964220047},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/513","is_oa":true,"landing_page_url":"https://doi.org/10.37236/513","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p26/pdf","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/513","is_oa":true,"landing_page_url":"https://doi.org/10.37236/513","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p26/pdf","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":null,"license_id":null,"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":[{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1516933281.pdf","grobid_xml":"https://content.openalex.org/works/W1516933281.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W83024883","https://openalex.org/W960859969","https://openalex.org/W1589331344","https://openalex.org/W1909201467","https://openalex.org/W1964610196","https://openalex.org/W1967237366","https://openalex.org/W1968769959","https://openalex.org/W2015292773","https://openalex.org/W2017418472","https://openalex.org/W2026897841","https://openalex.org/W2036811773","https://openalex.org/W2047785497","https://openalex.org/W2049335017","https://openalex.org/W2053898220","https://openalex.org/W2057661677","https://openalex.org/W2067182403","https://openalex.org/W2068380082","https://openalex.org/W2080740807","https://openalex.org/W2089188009","https://openalex.org/W2145501841","https://openalex.org/W2170438116","https://openalex.org/W2175167577","https://openalex.org/W2785506964","https://openalex.org/W2918018314","https://openalex.org/W2952251381","https://openalex.org/W2983896310","https://openalex.org/W3148190347","https://openalex.org/W6607110455","https://openalex.org/W6610169696"],"related_works":["https://openalex.org/W2391237956","https://openalex.org/W4311345810","https://openalex.org/W1506813909","https://openalex.org/W3169197204","https://openalex.org/W2380525562","https://openalex.org/W4291316360","https://openalex.org/W4297911588","https://openalex.org/W3004659243","https://openalex.org/W4229747356","https://openalex.org/W2539811847"],"abstract_inverted_index":{"The":[0,23,44],"chromatic":[1],"number":[2,11,26,32],"$\\chi(G)$":[3],"of":[4,12,18,21,33,42,64,68,121,137],"a":[5,15,135],"graph":[6,92],"$G$":[7],"is":[8,29,61,134],"the":[9,19,30,40,62,65,125,129],"minimum":[10,31],"colors":[13],"in":[14,51,73,110],"proper":[16],"coloring":[17],"vertices":[20],"$G$.":[22,43,69,93],"biclique":[24],"partition":[25,39],"${\\rm":[27,59],"bp}(G)$":[28],"complete":[34],"bipartite":[35],"subgraphs":[36],"whose":[37],"edges":[38],"edge-set":[41],"Rank-Coloring":[45,130],"Conjecture":[46,127],"(formulated":[47],"by":[48,75,98,140],"van":[49],"Nuffelen":[50],"1976)":[52],"states":[53],"that":[54,86],"$\\chi(G)\\leq":[55,87],"{\\rm":[56,88],"rank}(A(G))$,":[57],"where":[58],"rank}(A(G))$":[60],"rank":[63],"adjacency":[66],"matrix":[67],"This":[70,94],"was":[71,95],"disproved":[72,97],"1989":[74],"Alon":[76],"and":[77,83,100,128,142,144],"Seymour.":[78],"In":[79,113],"1991,":[80],"Alon,":[81],"Saks,":[82],"Seymour":[84],"conjectured":[85],"bp}(G)+1$":[89],"for":[90],"any":[91],"recently":[96],"Huang":[99,143],"Sudakov.":[101,145],"These":[102],"conjectures":[103],"are":[104],"also":[105],"related":[106],"to":[107,123],"interesting":[108],"problems":[109],"computational":[111],"complexity.":[112],"this":[114],"paper,":[115],"we":[116],"construct":[117],"new":[118],"infinite":[119],"families":[120],"counterexamples":[122],"both":[124],"Alon-Saks-Seymour":[126],"Conjecture.":[131],"Our":[132],"construction":[133],"generalization":[136],"similar":[138],"work":[139],"Razborov,":[141]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
