{"id":"https://openalex.org/W2898567807","doi":"https://doi.org/10.37236/706","title":"Asymptotic Behaviour of the Number of Eulerian Circuits","display_name":"Asymptotic Behaviour of the Number of Eulerian Circuits","publication_year":2011,"publication_date":"2011-11-14","ids":{"openalex":"https://openalex.org/W2898567807","doi":"https://doi.org/10.37236/706","mag":"2898567807"},"language":"en","primary_location":{"id":"doi:10.37236/706","is_oa":true,"landing_page_url":"https://doi.org/10.37236/706","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p219/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/v18i1p219/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035608597","display_name":"Mikhail Isaev","orcid":"https://orcid.org/0000-0002-5703-0951"},"institutions":[{"id":"https://openalex.org/I4210107641","display_name":"Centre de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/012e1xn46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210107641","https://openalex.org/I4210141950","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I153845743","display_name":"Moscow Institute of Physics and Technology","ror":"https://ror.org/00v0z9322","country_code":"RU","type":"education","lineage":["https://openalex.org/I153845743"]}],"countries":["FR","RU"],"is_corresponding":true,"raw_author_name":"Mikhail Isaev","raw_affiliation_strings":["Centre de Mathmatiques Appliques, Ecole Polytechnique 91128 Palaiseau, France","Moscow Institute of Physics and Technology 141700 Dolgoprudny, Russia","Centre de Math\u00e9matiques Appliqu\u00e9es, Ecole Polytechnique 91128 Palaiseau, France"],"affiliations":[{"raw_affiliation_string":"Centre de Mathmatiques Appliques, Ecole Polytechnique 91128 Palaiseau, France","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]},{"raw_affiliation_string":"Moscow Institute of Physics and Technology 141700 Dolgoprudny, Russia","institution_ids":["https://openalex.org/I153845743"]},{"raw_affiliation_string":"Centre de Math\u00e9matiques Appliqu\u00e9es, Ecole Polytechnique 91128 Palaiseau, France","institution_ids":["https://openalex.org/I4210107641","https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5035608597"],"corresponding_institution_ids":["https://openalex.org/I142476485","https://openalex.org/I153845743","https://openalex.org/I4210107641"],"apc_list":null,"apc_paid":null,"fwci":2.264,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.88543495,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"18","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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9998999834060669,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.8889063596725464},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.842354953289032},{"id":"https://openalex.org/keywords/algebraic-connectivity","display_name":"Algebraic connectivity","score":0.7917690277099609},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.7794564962387085},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6819952726364136},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6326698660850525},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6243022680282593},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.5788455605506897},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5092707872390747},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.48493292927742004},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.46904832124710083},{"id":"https://openalex.org/keywords/undirected-graph","display_name":"Undirected graph","score":0.44204720854759216},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.34937989711761475},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21846157312393188},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.2069835364818573},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16248109936714172}],"concepts":[{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.8889063596725464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.842354953289032},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.7917690277099609},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.7794564962387085},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6819952726364136},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6326698660850525},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6243022680282593},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5788455605506897},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5092707872390747},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.48493292927742004},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.46904832124710083},{"id":"https://openalex.org/C3018234147","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Undirected graph","level":3,"score":0.44204720854759216},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.34937989711761475},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21846157312393188},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.2069835364818573},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16248109936714172},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/706","is_oa":true,"landing_page_url":"https://doi.org/10.37236/706","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p219/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"}],"best_oa_location":{"id":"doi:10.37236/706","is_oa":true,"landing_page_url":"https://doi.org/10.37236/706","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p219/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/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2898567807.pdf","grobid_xml":"https://content.openalex.org/works/W2898567807.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1587744656","https://openalex.org/W1665320540","https://openalex.org/W2121163052","https://openalex.org/W2141731854","https://openalex.org/W2151417892","https://openalex.org/W2151718187","https://openalex.org/W2316063597","https://openalex.org/W2792874300","https://openalex.org/W2799004609","https://openalex.org/W3020856174","https://openalex.org/W4236189701"],"related_works":["https://openalex.org/W4205812024","https://openalex.org/W2597594164","https://openalex.org/W3046200067","https://openalex.org/W80320255","https://openalex.org/W2475700395","https://openalex.org/W2898567807","https://openalex.org/W4300664925","https://openalex.org/W2402951419","https://openalex.org/W2051180862","https://openalex.org/W4321593219"],"abstract_inverted_index":{"We":[0,26],"determine":[1],"the":[2,6,23,33],"asymptotic":[3],"behaviour":[4],"of":[5,8,22,32],"number":[7],"Eulerian":[9],"circuits":[10],"in":[11],"undirected":[12],"simple":[13],"graphs":[14],"with":[15],"large":[16],"algebraic":[17],"connectivity":[18],"(the":[19],"second-smallest":[20],"eigenvalue":[21],"Laplacian":[24,34],"matrix).":[25],"also":[27],"prove":[28],"some":[29],"new":[30],"properties":[31],"matrix.":[35]},"counts_by_year":[{"year":2017,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
