{"id":"https://openalex.org/W4408453090","doi":"https://doi.org/10.1007/s00493-025-00144-4","title":"Sets of r-Graphs that Color All r-Graphs","display_name":"Sets of r-Graphs that Color All r-Graphs","publication_year":2025,"publication_date":"2025-03-14","ids":{"openalex":"https://openalex.org/W4408453090","doi":"https://doi.org/10.1007/s00493-025-00144-4"},"language":"en","primary_location":{"id":"doi:10.1007/s00493-025-00144-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00144-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00144-4.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00144-4.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066109543","display_name":"Yulai Ma","orcid":"https://orcid.org/0000-0002-4324-3497"},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Yulai Ma","raw_affiliation_strings":["Department of Mathematics, Paderborn University, Warburger Str. 100, 33098, Paderborn, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Paderborn University, Warburger Str. 100, 33098, Paderborn, Germany","institution_ids":["https://openalex.org/I206945453"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001787916","display_name":"Davide Mattiolo","orcid":"https://orcid.org/0000-0001-5876-0887"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Davide Mattiolo","raw_affiliation_strings":["Department of Computer Science, KU Leuven Kulak, 8500, Kortrijk, Belgium"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, KU Leuven Kulak, 8500, Kortrijk, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041562341","display_name":"Eckhard Steffen","orcid":"https://orcid.org/0000-0002-9808-7401"},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Eckhard Steffen","raw_affiliation_strings":["Department of Mathematics, Paderborn University, Warburger Str. 100, 33098, Paderborn, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Paderborn University, Warburger Str. 100, 33098, Paderborn, Germany","institution_ids":["https://openalex.org/I206945453"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051639956","display_name":"Isaak H. Wolf","orcid":null},"institutions":[{"id":"https://openalex.org/I206945453","display_name":"Paderborn University","ror":"https://ror.org/058kzsd48","country_code":"DE","type":"education","lineage":["https://openalex.org/I206945453"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Isaak H. Wolf","raw_affiliation_strings":["Department of Mathematics, Paderborn University, Warburger Str. 100, 33098, Paderborn, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Paderborn University, Warburger Str. 100, 33098, Paderborn, Germany","institution_ids":["https://openalex.org/I206945453"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5066109543"],"corresponding_institution_ids":["https://openalex.org/I206945453"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05914227,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"45","issue":"2","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":0.9948999881744385,"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":0.9948999881744385,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9850999712944031,"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/mathematics","display_name":"Mathematics","score":0.8765881657600403},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8040449619293213},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.41840171813964844},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36078548431396484},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2941175699234009}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8765881657600403},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8040449619293213},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.41840171813964844},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36078548431396484},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2941175699234009}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00493-025-00144-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00144-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00144-4.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:20.500.12942/763914","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/20.500.12942/763914","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Combinatorica, vol. 45 (2), Art.No. ARTN 16","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1007/s00493-025-00144-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00493-025-00144-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00493-025-00144-4.pdf","source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324816","display_name":"Universit\u00e4t Paderborn","ror":"https://ror.org/058kzsd48"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4408453090.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W54441373","https://openalex.org/W1585499352","https://openalex.org/W1785620126","https://openalex.org/W1996149838","https://openalex.org/W2049716158","https://openalex.org/W2059233598","https://openalex.org/W2078493461","https://openalex.org/W2798912513","https://openalex.org/W2915215554","https://openalex.org/W2946135134","https://openalex.org/W2980927134","https://openalex.org/W3000684669","https://openalex.org/W3135430512","https://openalex.org/W3210257481","https://openalex.org/W4205617459","https://openalex.org/W4253850897","https://openalex.org/W4384931465","https://openalex.org/W4388372706"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2407258439","https://openalex.org/W2117608641","https://openalex.org/W2117848356","https://openalex.org/W2014290730","https://openalex.org/W416686103","https://openalex.org/W2149820269","https://openalex.org/W2072964213","https://openalex.org/W3021364183","https://openalex.org/W2408404065"],"abstract_inverted_index":{"Abstract":[0],"An":[1,32],"r":[2,7,23,30,62,70,106,113,323,333,340],"-regular":[3],"graph":[4,157],"is":[5,15,37,117,167,175,207,235,264,299],"an":[6,100,118,208,236,300],"-graph,":[8],"if":[9,163,212,282],"every":[10,77,111],"odd":[11],"set":[12,103,210],"of":[13,35,65,73,104,154,325,342],"vertices":[14],"connected":[16,105,112],"to":[17,69],"its":[18],"complement":[19],"by":[20],"at":[21],"least":[22],"edges.":[24],"Let":[25],"G":[26,36,66,115,136],"and":[27,211,278,328,335],"H":[28,33,74],"be":[29,99],"-graphs.":[31],"-coloring":[34],"a":[38,168],"mapping":[39],"$$f:E(G)":[40],"\\rightarrow":[41],"E(H)$$":[42],"<mml:math":[43,80,92,123,146,182,200,216,228,246,257,271,285,313],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[44,81,93,124,147,183,201,217,229,247,258,272,286,314],"<mml:mrow>":[45,82,125,184,190,218,248],"<mml:mi>f</mml:mi>":[46],"<mml:mo>:</mml:mo>":[47],"<mml:mi>E</mml:mi>":[48,53],"<mml:mo>(</mml:mo>":[49,54],"<mml:mi>G</mml:mi>":[50],"<mml:mo>)</mml:mo>":[51,56],"<mml:mo>\u2192</mml:mo>":[52],"<mml:mi>H</mml:mi>":[55,95,126,129,149,186,203,231,260,274,288,316],"</mml:mrow>":[57,86,132,194,195,222,252],"</mml:math>":[58,87,98,133,152,196,206,223,234,253,263,277,291,319],"such":[59,108],"that":[60,109,143,162,176,281,310],"each":[61],"adjacent":[63,71],"edges":[64,72],"are":[67],"mapped":[68],".":[75,137,159],"For":[76],"$$r\\ge":[78],"3$$":[79,245],"<mml:mi>r</mml:mi>":[83,96,130,219,232,249,261,275,289,317],"<mml:mo>\u2265</mml:mo>":[84,220,250],"<mml:mn>3</mml:mn>":[85,150,187,204,251],",":[88,224,254],"let":[89],"$$\\mathcal":[90,144,178,198,226,255,269,283,311],"H_r$$":[91,122,227,256,270,284,312],"<mml:msub>":[94,128,148,185,202,230,259,273,287,315],"</mml:msub>":[97,131,151,188,205,233,262,276,290,318],"inclusion-wise":[101],"minimal":[102],"-graphs,":[107,334],"for":[110,241],"-graph":[114],"there":[116],"$$H":[119],"\\in":[120],"\\mathcal":[121],"<mml:mo>\u2208</mml:mo>":[127],"which":[134],"colors":[135],"The":[138],"Petersen":[139,156],"Coloring":[140],"Conjecture":[141],"states":[142],"H_3$$":[145,199],"consists":[153],"the":[155,321,329,338],"P":[158],"We":[160,266],"show":[161,309],"true,":[164],"then":[165,225,279,297],"this":[166],"very":[169],"exclusive":[170],"situation.":[171],"Our":[172],"main":[173,306],"result":[174,307],"either":[177],"H_3":[179],"=":[180],"\\{P\\}$$":[181],"<mml:mo>=</mml:mo>":[189],"<mml:mo>{</mml:mo>":[191],"<mml:mi>P</mml:mi>":[192],"<mml:mo>}</mml:mo>":[193],"or":[197],"infinite":[209,237,301],"$$r":[213,243],"\\ge":[214,244],"4$$":[215],"<mml:mn>4</mml:mn>":[221],"set.":[238,302],"In":[239],"particular,":[240],"all":[242],"unique.":[265],"first":[267],"characterize":[268],"prove":[280],"contains":[292,320],"more":[293],"than":[294],"one":[295],"element,":[296],"it":[298],"To":[303],"obtain":[304],"our":[305],"we":[308,336],"smallest":[322,330,339],"-graphs":[324,341],"class":[326,343],"2":[327],"poorly":[331],"matchable":[332],"determine":[337],"2.":[344]},"counts_by_year":[],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}