{"id":"https://openalex.org/W2266082756","doi":"https://doi.org/10.37236/9944","title":"Discrete Quantitative Nodal Theorem","display_name":"Discrete Quantitative Nodal Theorem","publication_year":2021,"publication_date":"2021-09-23","ids":{"openalex":"https://openalex.org/W2266082756","doi":"https://doi.org/10.37236/9944","mag":"2266082756"},"language":"en","primary_location":{"id":"doi:10.37236/9944","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9944","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p58/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":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p58/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067889485","display_name":"L\u00e1szl\u00f3 Lov\u00e1sz","orcid":"https://orcid.org/0000-0002-6242-5894"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"L\u00e1szl\u00f3 Lov\u00e1sz","raw_affiliation_strings":["Alfred R\u00e9nyi Institute of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alfred R\u00e9nyi Institute of Mathematics","institution_ids":["https://openalex.org/I127817813"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5067889485"],"corresponding_institution_ids":["https://openalex.org/I127817813"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00132174,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"28","issue":"3","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":0.9987000226974487,"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":0.9987000226974487,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7789947986602783},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.7574031352996826},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7066589593887329},{"id":"https://openalex.org/keywords/nodal","display_name":"NODAL","score":0.5919091701507568},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.5022740364074707},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4640032649040222},{"id":"https://openalex.org/keywords/factor-theorem","display_name":"Factor theorem","score":0.429604172706604},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.4157117009162903},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3510527014732361},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3464208245277405},{"id":"https://openalex.org/keywords/fundamental-theorem","display_name":"Fundamental theorem","score":0.2827712893486023},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27452322840690613},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.0785001814365387},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07687082886695862}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7789947986602783},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.7574031352996826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7066589593887329},{"id":"https://openalex.org/C83330619","wikidata":"https://www.wikidata.org/wiki/Q21124872","display_name":"NODAL","level":2,"score":0.5919091701507568},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5022740364074707},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4640032649040222},{"id":"https://openalex.org/C40429337","wikidata":"https://www.wikidata.org/wiki/Q1108687","display_name":"Factor theorem","level":4,"score":0.429604172706604},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.4157117009162903},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3510527014732361},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3464208245277405},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.2827712893486023},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27452322840690613},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.0785001814365387},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07687082886695862},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105702510","wikidata":"https://www.wikidata.org/wiki/Q514","display_name":"Anatomy","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/9944","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9944","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p58/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:1601.06400","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1601.06400","pdf_url":"https://arxiv.org/pdf/1601.06400","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:2266082756","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1601.06400","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.1601.06400","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1601.06400","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.37236/9944","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9944","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v28i3p58/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":[{"display_name":"Reduced inequalities","score":0.6000000238418579,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2266082756.pdf","grobid_xml":"https://content.openalex.org/works/W2266082756.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1631603072","https://openalex.org/W1993111701","https://openalex.org/W1997066757","https://openalex.org/W2013317554","https://openalex.org/W2106285343","https://openalex.org/W2107940287","https://openalex.org/W2120899029","https://openalex.org/W6603395654"],"related_works":["https://openalex.org/W3202967365","https://openalex.org/W3023017559","https://openalex.org/W1992363721","https://openalex.org/W1880047185","https://openalex.org/W2180586453","https://openalex.org/W2530848635","https://openalex.org/W2154299480","https://openalex.org/W2344614906","https://openalex.org/W2187056206","https://openalex.org/W2040753208","https://openalex.org/W2528364415","https://openalex.org/W2322827169","https://openalex.org/W2767886788","https://openalex.org/W2289654433","https://openalex.org/W1976991503","https://openalex.org/W2739185624","https://openalex.org/W3101233038","https://openalex.org/W2086253178","https://openalex.org/W1633370051","https://openalex.org/W73868553"],"abstract_inverted_index":{"We":[0],"prove":[1],"a":[2,10,72],"theorem":[3],"that":[4,34],"can":[5],"be":[6],"thought":[7],"of":[8,13,29,41,59],"as":[9],"common":[11],"generalization":[12],"the":[14,36,42,50,54,60],"Discrete":[15],"Nodal":[16],"Theorem":[17],"and":[18,38,56],"(one":[19],"direction":[20],"of)":[21],"Cheeger's":[22],"Inequality":[23],"for":[24],"graphs.":[25],"A":[26],"special":[27],"case":[28],"this":[30],"result":[31],"will":[32],"assert":[33],"if":[35],"second":[37],"third":[39],"eigenvalues":[40],"Laplacian":[43],"are":[44,65],"at":[45],"least":[46],"$\\varepsilon$":[47],"apart,":[48],"then":[49],"subgraphs":[51],"induced":[52],"by":[53],"positive":[55],"negative":[57],"supports":[58],"eigenvector":[61],"belonging":[62],"to":[63],"$\\lambda_2$":[64],"not":[66],"only":[67],"connected,":[68],"but":[69],"edge-expanders":[70],"(in":[71],"weighted":[73],"sense,":[74],"with":[75],"expansion":[76],"depending":[77],"on":[78],"$\\varepsilon$).":[79]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
