{"id":"https://openalex.org/W2951441491","doi":"https://doi.org/10.37236/7753","title":"On Degree Properties of Crossing-Critical Families of Graphs","display_name":"On Degree Properties of Crossing-Critical Families of Graphs","publication_year":2019,"publication_date":"2019-03-22","ids":{"openalex":"https://openalex.org/W2951441491","doi":"https://doi.org/10.37236/7753","mag":"2951441491"},"language":"en","primary_location":{"id":"doi:10.37236/7753","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7753","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i1p53/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i1p53/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037779732","display_name":"Drago Bokal","orcid":"https://orcid.org/0000-0003-1196-5476"},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Drago Bokal","raw_affiliation_strings":["University of Maribor","Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia"],"affiliations":[{"raw_affiliation_string":"University of Maribor","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074006207","display_name":"Mojca Bra\u010di\u010d","orcid":null},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Mojca Bra\u010di\u010d","raw_affiliation_strings":["University of Maribor","Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia"],"affiliations":[{"raw_affiliation_string":"University of Maribor","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics, University of Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031262808","display_name":"Marek Der\u0148\u00e1r","orcid":null},"institutions":[{"id":"https://openalex.org/I21449261","display_name":"Masaryk University","ror":"https://ror.org/02j46qs45","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21449261"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Marek Der\u0148\u00e1r","raw_affiliation_strings":["Masaryk University","Faculty of informatics, Masaryk University, Brno, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Masaryk University","institution_ids":["https://openalex.org/I21449261"]},{"raw_affiliation_string":"Faculty of informatics, Masaryk University, Brno, Czech Republic","institution_ids":["https://openalex.org/I21449261"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090886391","display_name":"Petr Hlin\u011bn\u00fd","orcid":"https://orcid.org/0000-0003-2125-1514"},"institutions":[{"id":"https://openalex.org/I21449261","display_name":"Masaryk University","ror":"https://ror.org/02j46qs45","country_code":"CZ","type":"education","lineage":["https://openalex.org/I21449261"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Petr Hlin\u011bn\u00fd","raw_affiliation_strings":["Masaryk University","Faculty of informatics, Masaryk University, Brno, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Masaryk University","institution_ids":["https://openalex.org/I21449261"]},{"raw_affiliation_string":"Faculty of informatics, Masaryk University, Brno, Czech Republic","institution_ids":["https://openalex.org/I21449261"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5037779732"],"corresponding_institution_ids":["https://openalex.org/I37696226"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0892844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":"1","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":0.9998000264167786,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9973999857902527,"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":0.9973000288009644,"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":0.6956823468208313},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6828988790512085},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6461473703384399},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5832126140594482},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.465107262134552},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4379901885986328},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4112360179424286},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3620138466358185},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1992906630039215},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14324980974197388}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6956823468208313},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6828988790512085},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6461473703384399},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5832126140594482},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.465107262134552},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4379901885986328},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4112360179424286},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3620138466358185},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1992906630039215},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14324980974197388},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/7753","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7753","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i1p53/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1803.10509","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1803.10509","pdf_url":"https://arxiv.org/pdf/1803.10509","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2951441491","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1803.10509","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1803.10509","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1803.10509","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/7753","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7753","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i1p53/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1022138827","display_name":null,"funder_award_id":"17-00837S","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G2169906750","display_name":null,"funder_award_id":"N1-0057","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G2460596887","display_name":null,"funder_award_id":"P1-0297","funder_id":"https://openalex.org/F4320321006","funder_display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky"},{"id":"https://openalex.org/G3894112125","display_name":null,"funder_award_id":"P1-0297","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G4172136535","display_name":null,"funder_award_id":"L7-5459","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G6728495609","display_name":null,"funder_award_id":"J1-8130","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G8112475816","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"}],"funders":[{"id":"https://openalex.org/F4320321006","display_name":"Grantov\u00e1 Agentura \u010cesk\u00e9 Republiky","ror":"https://ror.org/01pv73b02"},{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2951441491.pdf","grobid_xml":"https://content.openalex.org/works/W2951441491.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W4007448","https://openalex.org/W1500859847","https://openalex.org/W1983496943","https://openalex.org/W1987717724","https://openalex.org/W1999834983","https://openalex.org/W2000808638","https://openalex.org/W2006582264","https://openalex.org/W2018300730","https://openalex.org/W2033843939","https://openalex.org/W2056837081","https://openalex.org/W2068148652","https://openalex.org/W2083735231","https://openalex.org/W2083875786","https://openalex.org/W2099137080","https://openalex.org/W2110315734","https://openalex.org/W2112497773","https://openalex.org/W2140619995","https://openalex.org/W2751852392","https://openalex.org/W4243779214","https://openalex.org/W6600579306","https://openalex.org/W6647476779","https://openalex.org/W6658981832","https://openalex.org/W6725025681"],"related_works":["https://openalex.org/W3159665485","https://openalex.org/W2137702369","https://openalex.org/W3176308333","https://openalex.org/W3081895225","https://openalex.org/W2298083910","https://openalex.org/W2082512371","https://openalex.org/W3174257859","https://openalex.org/W2506696544","https://openalex.org/W1966637575","https://openalex.org/W3095896901","https://openalex.org/W2898773895","https://openalex.org/W1980071981","https://openalex.org/W2079721544","https://openalex.org/W2951650328","https://openalex.org/W3098553937","https://openalex.org/W2079314478","https://openalex.org/W2915433562","https://openalex.org/W2886253980","https://openalex.org/W2951461810","https://openalex.org/W1995396946"],"abstract_inverted_index":{"Answering":[0],"an":[1],"open":[2],"question":[3],"from":[4],"2007,":[5],"we":[6,30,69],"construct":[7],"infinite":[8,35],"$k$-crossing-critical":[9,94,133],"families":[10,36,43,49,134],"of":[11,16,34,37,64,75,115],"graphs":[12,38,114],"that":[13,79,97,107],"contain":[14],"vertices":[15],"any":[17,22,73,87,137],"prescribed":[18],"odd":[19],"degree,":[20],"for":[21,72,86,136],"sufficiently":[23,88,138],"large":[24,89,139],"$k$.":[25,140],"To":[26],"answer":[27,59],"this":[28,116],"question,":[29],"introduce":[31],"several":[32],"properties":[33],"and":[39,82,85,123],"operations":[40],"on":[41,62],"the":[42,98,104,128],"allowing":[44],"us":[45,57],"to":[46,58],"obtain":[47],"new":[48],"preserving":[50],"those":[51],"properties.":[52],"This":[53],"conceptual":[54],"setup":[55],"allows":[56],"general":[60],"questions":[61],"behaviour":[63],"degrees":[65,106],"in":[66,100,111,127],"crossing-critical":[67],"graphs:":[68],"show":[70],"that,":[71],"set":[74],"integers":[76],"$D$":[77,101,122],"such":[78,96],"$\\min(D)\\geq":[80],"3$":[81],"$3,4\\in":[83],"D$,":[84],"$k$,":[90],"there":[91],"exists":[92],"a":[93],"family":[95],"numbers":[99],"are":[102,131],"precisely":[103],"vertex":[105],"occur":[108],"arbitrarily":[109],"often":[110],"(large":[112],"enough)":[113],"family.":[117],"Furthermore,":[118],"even":[119],"if":[120],"both":[121],"some":[124],"average":[125],"degree":[126],"interval":[129],"$(3,6)$":[130],"prescribed,":[132],"exist":[135]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
