{"id":"https://openalex.org/W2052268721","doi":"https://doi.org/10.2478/v10037-011-0005-6","title":"The Mycielskian of a Graph","display_name":"The Mycielskian of a Graph","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2052268721","doi":"https://doi.org/10.2478/v10037-011-0005-6","mag":"2052268721"},"language":"pl","primary_location":{"id":"doi:10.2478/v10037-011-0005-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0005-6","pdf_url":null,"source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.2478/v10037-011-0005-6","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052948222","display_name":"Piotr Rudnicki","orcid":null},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Piotr Rudnicki","raw_affiliation_strings":["University of Alberta, Edmonton, Canad\u00c3\u00a1"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Alberta, Edmonton, Canad\u00c3\u00a1","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036977647","display_name":"Lorna Stewart","orcid":null},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Lorna Stewart","raw_affiliation_strings":["University of Alberta, Edmonton, Canad\u00c3\u00a1"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Alberta, Edmonton, Canad\u00c3\u00a1","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I154425047"],"apc_list":null,"apc_paid":null,"fwci":0.6381,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.69510078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"19","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9997000098228455,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9997000098228455,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9923999905586243,"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":0.9761999845504761,"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":0.6548033356666565},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4168073236942291},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.326923131942749},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.30381226539611816},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2598806619644165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6548033356666565},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4168073236942291},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.326923131942749},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.30381226539611816},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2598806619644165}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.2478/v10037-011-0005-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0005-6","pdf_url":null,"source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.228.2592","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.228.2592","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://mizar.org/fm/2011-19/pdf19-1/mycielsk.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:18a0ae6de6f8437b89dd110dbb8e1133","is_oa":true,"landing_page_url":"https://doaj.org/article/18a0ae6de6f8437b89dd110dbb8e1133","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Formalized Mathematics, Vol 19, Iss 1, Pp 27-34 (2011)","raw_type":"article"},{"id":"pmh:oai:repozytorium.uwb.edu.pl:11320/3592","is_oa":false,"landing_page_url":"http://hdl.handle.net/11320/3592","pdf_url":null,"source":{"id":"https://openalex.org/S4306400933","display_name":"The Repository of University in Bialystok (University in Bialystok)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210094198","host_organization_name":"University Clinical Hospital In Bialystok","host_organization_lineage":["https://openalex.org/I4210094198"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.2478/v10037-011-0005-6","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10037-011-0005-6","pdf_url":null,"source":{"id":"https://openalex.org/S179241345","display_name":"Formalized Mathematics","issn_l":"1426-2630","issn":["1426-2630","1898-9934"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Formalized Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W180239714","https://openalex.org/W192809544","https://openalex.org/W260340778","https://openalex.org/W2105559527","https://openalex.org/W2115474581","https://openalex.org/W2126517143","https://openalex.org/W2138492341","https://openalex.org/W2163641194","https://openalex.org/W2166565522","https://openalex.org/W2170803232","https://openalex.org/W2296232473","https://openalex.org/W2304533832","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"The":[0,43],"Mycielskian":[1,65],"of":[2,16,50,66,103,107],"a":[3,17,23,30,67],"GraphLet":[4],"\u03c9(G)":[5,81],"and":[6,12,75,82,112,116],"\u03c7(G)":[7,40,85],"be":[8],"the":[9,13,47,60,64,72,101],"clique":[10,115],"number":[11,15],"chromatic":[14,117],"graph":[18,31,49,68,93],"G.":[19],"Mycielski":[20],"[11]":[21],"presented":[22],"construction":[24],"that":[25,78],"for":[26,91],"any":[27],"n":[28,111],"creates":[29],"Mn":[32,58,105],"which":[33],"is":[34,46,55,89],"triangle-free":[35],"(\u03c9(G)":[36],"=":[37,80,84],"2)":[38],"with":[39],">":[41],"n.":[42],"starting":[44],"point":[45],"complete":[48],"two":[51],"vertices":[52],"(K2).":[53],"M(n+1)":[54],"obtained":[56],"from":[57],"through":[59],"operation":[61,73],"\u03bc(G)":[62,74],"called":[63],"G.We":[69],"first":[70],"define":[71,100],"then":[76],"show":[77],"\u03c9(\u03bc(G))":[79],"\u03c7(\u03bc(G))":[83],"+":[86],"1.":[87],"This":[88],"done":[90],"arbitrary":[92],"G,":[94],"see":[95],"also":[96],"[10].":[97],"Then":[98],"we":[99],"sequence":[102],"graphs":[104],"each":[106],"exponential":[108],"size":[109],"in":[110],"give":[113],"their":[114],"numbers.":[118]},"counts_by_year":[{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}