{"id":"https://openalex.org/W1606591565","doi":"https://doi.org/10.37236/5321","title":"Average Degree Conditions Forcing a Minor","display_name":"Average Degree Conditions Forcing a Minor","publication_year":2016,"publication_date":"2016-03-04","ids":{"openalex":"https://openalex.org/W1606591565","doi":"https://doi.org/10.37236/5321","mag":"1606591565"},"language":"en","primary_location":{"id":"doi:10.37236/5321","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5321","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p42/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":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p42/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018558486","display_name":"Daniel J. Harvey","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Daniel J. Harvey","raw_affiliation_strings":["School of Mathematical Sciences\r\nMonash University","School of Mathematical Sciences#R##N#Monash University"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences\r\nMonash University","institution_ids":[]},{"raw_affiliation_string":"School of Mathematical Sciences#R##N#Monash University","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066302647","display_name":"David R. Wood","orcid":"https://orcid.org/0000-0001-8866-3041"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"David R. Wood","raw_affiliation_strings":["School of Mathematical Sciences\r\nMonash University","School of Mathematical Sciences#R##N#Monash University"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences\r\nMonash University","institution_ids":[]},{"raw_affiliation_string":"School of Mathematical Sciences#R##N#Monash University","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018558486"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7009,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.87546887,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"23","issue":"1","first_page":null,"last_page":null},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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/T11476","display_name":"Graph theory and applications","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.816717803478241},{"id":"https://openalex.org/keywords/minor","display_name":"Minor (academic)","score":0.7628518342971802},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7356064319610596},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6962929964065552},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6440932750701904},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6248697638511658},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5921455025672913},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3645380735397339}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.816717803478241},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.7628518342971802},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7356064319610596},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6962929964065552},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6440932750701904},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6248697638511658},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5921455025672913},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3645380735397339},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/5321","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5321","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p42/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"}],"best_oa_location":{"id":"doi:10.37236/5321","is_oa":true,"landing_page_url":"https://doi.org/10.37236/5321","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v23i1p42/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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.44999998807907104}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1606591565.pdf","grobid_xml":"https://content.openalex.org/works/W1606591565.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W48717235","https://openalex.org/W49540560","https://openalex.org/W1967546560","https://openalex.org/W1979717362","https://openalex.org/W1989340449","https://openalex.org/W1991445030","https://openalex.org/W1997241423","https://openalex.org/W2029404717","https://openalex.org/W2047993669","https://openalex.org/W2065163524","https://openalex.org/W2120650079","https://openalex.org/W2132418889","https://openalex.org/W2151438396","https://openalex.org/W2161040448","https://openalex.org/W2161786935","https://openalex.org/W2162070115","https://openalex.org/W2170136611","https://openalex.org/W2170758948","https://openalex.org/W2487536192","https://openalex.org/W2504259738","https://openalex.org/W3098569837","https://openalex.org/W4205775268"],"related_works":["https://openalex.org/W2368619281","https://openalex.org/W2377143628","https://openalex.org/W2355995962","https://openalex.org/W2371352078","https://openalex.org/W2392462513","https://openalex.org/W2362718971","https://openalex.org/W2368173763","https://openalex.org/W2977970519","https://openalex.org/W191560551","https://openalex.org/W2075931614"],"abstract_inverted_index":{"Mader":[0],"first":[1],"proved":[2],"that":[3],"high":[4,87],"average":[5,25,42,72],"degree":[6,26,43,73,88],"forces":[7],"a":[8,12,30,34,52,60,82,104],"given":[9],"graph":[10,32,49,84],"as":[11,33,51],"minor.":[13,35,53],"Often":[14],"motivated":[15],"by":[16,63],"Hadwiger's":[17],"Conjecture,":[18],"much":[19],"research":[20],"has":[21],"focused":[22],"on":[23,70],"the":[24,41,71],"required":[27,44,74],"to":[28,45,75],"force":[29,46,76],"complete":[31,114],"Subsequently,":[36],"various":[37],"authors":[38],"have":[39],"considered":[40],"an":[47,77,92,112],"arbitrary":[48],"$H$":[50,80,110],"Here,":[54],"we":[55],"strengthen":[56],"(under":[57],"certain":[58],"conditions)":[59],"recent":[61],"result":[62],"Reed":[64,96],"and":[65,97,99],"Wood,":[66,98],"giving":[67],"better":[68],"bounds":[69],"$H$-minor":[78],"when":[79,109],"is":[81,111],"sparse":[83],"with":[85],"many":[86],"vertices.":[89],"This":[90],"solves":[91],"open":[93],"problem":[94],"of":[95],"also":[100],"generalises":[101],"(to":[102],"within":[103],"constant":[105],"factor)":[106],"known":[107],"results":[108],"unbalanced":[113],"bipartite":[115],"graph.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
