{"id":"https://openalex.org/W2011835719","doi":"https://doi.org/10.1017/s0963548306007899","title":"Ore-type graph packing problems","display_name":"Ore-type graph packing problems","publication_year":2006,"publication_date":"2006-09-20","ids":{"openalex":"https://openalex.org/W2011835719","doi":"https://doi.org/10.1017/s0963548306007899","mag":"2011835719"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548306007899","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306007899","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","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/A5080894223","display_name":"Alexandr Kostochka","orcid":"https://orcid.org/0000-0002-6363-3804"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I4210118319","display_name":"Scientific Research Institute of Biochemistry","ror":"https://ror.org/02y0e7413","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210118319"]},{"id":"https://openalex.org/I4210148457","display_name":"Institute of Applied Physics","ror":"https://ror.org/05518k367","country_code":"RU","type":"other","lineage":["https://openalex.org/I4210148457"]}],"countries":["RU","US"],"is_corresponding":false,"raw_author_name":"A. V. KOSTOCHKA","raw_affiliation_strings":["Department of Mathematics, University of Illinois, Urbana, IL 61801, USA","Institute of Mathematics, Novosibirsk, 630090, Russia (e-mail:","Department of Mathematics, University of Illinois, Urbana, IL 61801, USA and Institute of Mathematics, Novosibirsk, 630090, Russia (e-mail: kostochk@math.uiuc.edu, gexinyu@math.uiuc.edu)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, IL 61801, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Institute of Mathematics, Novosibirsk, 630090, Russia (e-mail:","institution_ids":["https://openalex.org/I4210118319","https://openalex.org/I4210148457"]},{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, IL 61801, USA and Institute of Mathematics, Novosibirsk, 630090, Russia (e-mail: kostochk@math.uiuc.edu, gexinyu@math.uiuc.edu)","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077977616","display_name":"Gexin Yu","orcid":"https://orcid.org/0000-0001-5898-7344"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G. YU","raw_affiliation_strings":["Department of Mathematics, University of Illinois, Urbana, IL 61801, USA","Dept. of Mathematics, University of Illinois, Urbana, IL 61801, USA#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Illinois, Urbana, IL 61801, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Dept. of Mathematics, University of Illinois, Urbana, IL 61801, USA#TAB#","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.8393,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.89768421,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"16","issue":"1","first_page":"167","last_page":"169"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9995999932289124,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9962999820709229,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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":0.8067994117736816},{"id":"https://openalex.org/keywords/injective-function","display_name":"Injective function","score":0.7048513889312744},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6857949495315552},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5625501275062561},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5487551689147949},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.42496562004089355},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.07493844628334045}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8067994117736816},{"id":"https://openalex.org/C128107574","wikidata":"https://www.wikidata.org/wiki/Q182003","display_name":"Injective function","level":2,"score":0.7048513889312744},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6857949495315552},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5625501275062561},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5487551689147949},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.42496562004089355},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07493844628334045},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548306007899","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548306007899","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.224.6870","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.224.6870","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.uiuc.edu/%7Ekostochk/docs/2008/cpc06y.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1971367602","https://openalex.org/W2015832457","https://openalex.org/W2035089435","https://openalex.org/W2082497622"],"related_works":["https://openalex.org/W1492157759","https://openalex.org/W2655188380","https://openalex.org/W2963000151","https://openalex.org/W3111310291","https://openalex.org/W2742781961","https://openalex.org/W1656421143","https://openalex.org/W2962729062","https://openalex.org/W2886974128","https://openalex.org/W2811294698","https://openalex.org/W2239937566"],"abstract_inverted_index":{"We":[0],"say":[1],"that":[2,24],"$n$":[3,53],"-vertex":[4,54],"graphs":[5,45,55],"$G_1,G_2,\\ldots,G_k$":[6],"pack":[7,59],"if":[8,60,63],"there":[9],"exist":[10],"injective":[11],"mappings":[12],"of":[13,27,36,68,72],"their":[14],"vertex":[15],"sets":[16,30],"onto":[17],"$[n]":[18],"=":[19],"\\{1,":[20],"\\ldots,n":[21],"\\}$":[22],"such":[23],"the":[25,28,69],"images":[26],"edge":[29],"do":[31],"not":[32],"intersect.":[33],"The":[34],"notion":[35],"packing":[37],"allows":[38],"one":[39],"to":[40],"make":[41],"some":[42],"problems":[43],"on":[44],"more":[46,49],"natural":[47],"or":[48],"general.":[50],"Clearly,":[51],"two":[52],"$G_1$":[56,64],"and":[57,61],"$G_2$":[58,73],"only":[62],"is":[65],"a":[66],"subgraph":[67],"complement":[70],"$\\overline{G}_2$":[71],".":[74]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}