{"id":"https://openalex.org/W1558974145","doi":"https://doi.org/10.37236/131","title":"Near Threshold Graphs","display_name":"Near Threshold Graphs","publication_year":2009,"publication_date":"2009-03-25","ids":{"openalex":"https://openalex.org/W1558974145","doi":"https://doi.org/10.37236/131","mag":"1558974145"},"language":"en","primary_location":{"id":"doi:10.37236/131","is_oa":true,"landing_page_url":"https://doi.org/10.37236/131","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r42/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":null,"license_id":null,"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/v16i1r42/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058163539","display_name":"Steve Kirkland","orcid":"https://orcid.org/0000-0002-9496-5553"},"institutions":[{"id":"https://openalex.org/I194028371","display_name":"University of Regina","ror":"https://ror.org/03dzc0485","country_code":"CA","type":"education","lineage":["https://openalex.org/I194028371"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Steve Kirkland","raw_affiliation_strings":["Department of Mathematics and Statistics","University of Regina Regina, Saskatchewan, Canada S4S 0A2"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics","institution_ids":[]},{"raw_affiliation_string":"University of Regina Regina, Saskatchewan, Canada S4S 0A2","institution_ids":["https://openalex.org/I194028371"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5058163539"],"corresponding_institution_ids":["https://openalex.org/I194028371"],"apc_list":null,"apc_paid":null,"fwci":0.7712,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65740907,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":1.0,"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"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9970999956130981,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9948999881744385,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8345633745193481},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.825263261795044},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.7579309940338135},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6726946234703064},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.6632164120674133},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5305488705635071},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.49563682079315186},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4402671456336975},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4320669174194336},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07178372144699097},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04756927490234375}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8345633745193481},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.825263261795044},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7579309940338135},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6726946234703064},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.6632164120674133},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5305488705635071},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.49563682079315186},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4402671456336975},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4320669174194336},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07178372144699097},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04756927490234375},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/131","is_oa":true,"landing_page_url":"https://doi.org/10.37236/131","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r42/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:eprints.maynoothuniversity.ie:1642","is_oa":true,"landing_page_url":null,"pdf_url":"http://eprints.maynoothuniversity.ie/1642/1/HamiltonNearThreshold.pdf","source":{"id":"https://openalex.org/S4306401432","display_name":"Maynooth University ePrints and eTheses Archive (Maynooth University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I157286207","host_organization_name":"National University of Ireland, Maynooth","host_organization_lineage":["https://openalex.org/I157286207"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.160.3369","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.3369","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_16/PDF/v16i1r42.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/131","is_oa":true,"landing_page_url":"https://doi.org/10.37236/131","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r42/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","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":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1558974145.pdf","grobid_xml":"https://content.openalex.org/works/W1558974145.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1968625658","https://openalex.org/W1998018314","https://openalex.org/W2006148496","https://openalex.org/W2008194408","https://openalex.org/W2027734096","https://openalex.org/W2028775537","https://openalex.org/W2035868960","https://openalex.org/W2093473133","https://openalex.org/W2123880758","https://openalex.org/W2128448454","https://openalex.org/W2144267444","https://openalex.org/W2144752643","https://openalex.org/W2610857016","https://openalex.org/W2987651166"],"related_works":["https://openalex.org/W2951695430","https://openalex.org/W4300891849","https://openalex.org/W2318687609","https://openalex.org/W91590591","https://openalex.org/W94411513","https://openalex.org/W2377770720","https://openalex.org/W159772521","https://openalex.org/W2113626999","https://openalex.org/W4311883357","https://openalex.org/W2950100995"],"abstract_inverted_index":{"A":[0],"conjecture":[1,25],"of":[2,29,60],"Grone":[3],"and":[4,34,36,48,67],"Merris":[5,37],"states":[6],"that":[7],"for":[8,43,64],"any":[9],"graph":[10],"$G$,":[11],"its":[12,19],"Laplacian":[13],"spectrum,":[14],"$\\Lambda(G)$,":[15],"is":[16],"majorized":[17],"by":[18],"conjugate":[20],"degree":[21],"sequence,":[22],"$D^*(G)$.":[23],"That":[24],"prompts":[26],"an":[27],"investigation":[28],"the":[30,40,45,61],"relationship":[31],"between":[32],"$\\Lambda(G)$":[33,47,66],"$D^*(G),$":[35],"has":[38],"characterized":[39],"graphs":[41,62],"$G$":[42,63],"which":[44,65],"multisets":[46],"$D^*(G)$":[49,68],"are":[50],"equal.":[51],"In":[52],"this":[53],"paper,":[54],"we":[55],"provide":[56],"a":[57],"constructive":[58],"characterization":[59],"share":[69],"all":[70],"but":[71],"two":[72],"elements.":[73]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
