{"id":"https://openalex.org/W2507610879","doi":"https://doi.org/10.1137/17m1115320","title":"The Crossing Number of the Cone of a Graph","display_name":"The Crossing Number of the Cone of a Graph","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2507610879","doi":"https://doi.org/10.1137/17m1115320","mag":"2507610879"},"language":"en","primary_location":{"id":"doi:10.1137/17m1115320","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1115320","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-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/A5063863965","display_name":"Carlos A. Alfaro","orcid":"https://orcid.org/0000-0001-9783-8587"},"institutions":[{"id":"https://openalex.org/I29300151","display_name":"Bank of Mexico","ror":"https://ror.org/02xp9d883","country_code":"MX","type":"other","lineage":["https://openalex.org/I29300151"]}],"countries":["MX"],"is_corresponding":true,"raw_author_name":"Carlos A. Alfaro","raw_affiliation_strings":["Banco de M\u00e9xico, Ciudad de M\u00e9xico, M\u00e9xico"],"affiliations":[{"raw_affiliation_string":"Banco de M\u00e9xico, Ciudad de M\u00e9xico, M\u00e9xico","institution_ids":["https://openalex.org/I29300151"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055821136","display_name":"Alan Arroyo","orcid":"https://orcid.org/0000-0003-2401-8670"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Alan Arroyo","raw_affiliation_strings":["Department of Combinatorics and Optimization, University of Waterloo, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Combinatorics and Optimization, University of Waterloo, Canada","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031262808","display_name":"Marek Der\u0148\u00e1r","orcid":null},"institutions":[{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]},{"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","SI"],"is_corresponding":false,"raw_author_name":"Marek Der\u0148\u00e1r","raw_affiliation_strings":["Department of Mathematics, Ljubljana, Slovenia","Faculty of Informatics, Masaryk University, Brno, Czech Republic"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ljubljana, Slovenia","institution_ids":["https://openalex.org/I4210106342"]},{"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/A5005993212","display_name":"Bojan Mohar","orcid":"https://orcid.org/0000-0002-7408-6148"},"institutions":[{"id":"https://openalex.org/I18014758","display_name":"Simon Fraser University","ror":"https://ror.org/0213rcc28","country_code":"CA","type":"education","lineage":["https://openalex.org/I18014758"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Bojan Mohar","raw_affiliation_strings":["Department of Mathematics, Simon Fraser University, Burnaby, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Simon Fraser University, Burnaby, Canada","institution_ids":["https://openalex.org/I18014758"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063863965"],"corresponding_institution_ids":["https://openalex.org/I29300151"],"apc_list":null,"apc_paid":null,"fwci":0.4275,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.62127166,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"32","issue":"3","first_page":"2080","last_page":"2093"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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":0.9993000030517578,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8857808113098145},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8572999238967896},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6998358964920044},{"id":"https://openalex.org/keywords/crossing-number","display_name":"Crossing number (knot theory)","score":0.6814146637916565},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.627072274684906},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5930547118186951},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.503757655620575},{"id":"https://openalex.org/keywords/cone","display_name":"Cone (formal languages)","score":0.47281065583229065},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.47234049439430237},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4043402075767517},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06103426218032837}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8857808113098145},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8572999238967896},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6998358964920044},{"id":"https://openalex.org/C2777724877","wikidata":"https://www.wikidata.org/wiki/Q2548661","display_name":"Crossing number (knot theory)","level":3,"score":0.6814146637916565},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.627072274684906},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5930547118186951},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.503757655620575},{"id":"https://openalex.org/C30014739","wikidata":"https://www.wikidata.org/wiki/Q5159445","display_name":"Cone (formal languages)","level":2,"score":0.47281065583229065},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.47234049439430237},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4043402075767517},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06103426218032837},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/17m1115320","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1115320","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2272278055","display_name":null,"funder_award_id":"166059","funder_id":"https://openalex.org/F4320321739","funder_display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda"},{"id":"https://openalex.org/G8595721295","display_name":null,"funder_award_id":"NSERC","funder_id":"https://openalex.org/F4320320994","funder_display_name":"Canada Research Chairs"}],"funders":[{"id":"https://openalex.org/F4320320994","display_name":"Canada Research Chairs","ror":"https://ror.org/0517h6h17"},{"id":"https://openalex.org/F4320321739","display_name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","ror":"https://ror.org/059ex5q34"},{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"},{"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":10,"referenced_works":["https://openalex.org/W13988344","https://openalex.org/W1484234729","https://openalex.org/W1965094948","https://openalex.org/W1990541441","https://openalex.org/W2034842587","https://openalex.org/W2038562737","https://openalex.org/W2046344201","https://openalex.org/W2109042433","https://openalex.org/W2109717525","https://openalex.org/W2117566233"],"related_works":["https://openalex.org/W3005679577","https://openalex.org/W2611334166","https://openalex.org/W2751086833","https://openalex.org/W2731724293","https://openalex.org/W2347260277","https://openalex.org/W2003305701","https://openalex.org/W2025517193","https://openalex.org/W2963920438","https://openalex.org/W2104330975","https://openalex.org/W3003396734"],"abstract_inverted_index":{"Motivated":[0],"by":[1,5,8,39],"a":[2,23,41,93],"problem":[3,120],"asked":[4],"Richter":[6],"and":[7,26,101,126],"the":[9,16,19,27,34,47,55,74,86,119],"long":[10],"standing":[11],"Harary--Hill":[12],"conjecture,":[13],"we":[14,69,112],"study":[15],"relation":[17],"between":[18],"crossing":[20,28,96,104],"number":[21,29,97,105],"of":[22,30,110,116],"graph":[24,35,94],"$G$":[25,38],"its":[31],"cone":[32,102],"$CG$,":[33],"obtained":[36],"from":[37],"adding":[40],"new":[42],"vertex":[43],"adjacent":[44],"to":[45,123],"all":[46],"vertices":[48],"in":[49,72],"$G$.":[50],"Simple":[51],"examples":[52],"show":[53,127],"that":[54,78,128],"difference":[56],"$cr(CG)-cr(G)$":[57],"can":[58],"be":[59],"arbitrarily":[60],"large":[61],"for":[62,80,89],"any":[63],"fixed":[64],"$k=cr(G)$.":[65],"In":[66],"this":[67],"work,":[68],"are":[70,135],"interested":[71],"finding":[73],"smallest":[75,87],"possible":[76],"difference;":[77],"is,":[79],"each":[81],"nonnegative":[82],"integer":[83],"$k$,":[84,111],"find":[85],"$f(k)$":[88,117],"which":[90],"there":[91],"exists":[92],"with":[95,103],"at":[98],"least":[99],"$k$":[100],"$f(k)$.":[106],"For":[107],"small":[108],"values":[109,115],"give":[113],"exact":[114],"when":[118,132],"is":[121],"restricted":[122],"simple":[124],"graphs":[125],"$f(k)=k+\\Theta":[129],"(\\sqrt":[130],"{k})$":[131],"multiple":[133],"edges":[134],"allowed.":[136]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}