{"id":"https://openalex.org/W2000198292","doi":"https://doi.org/10.1007/s00453-013-9766-3","title":"Inequalities for the Number of Walks in Graphs","display_name":"Inequalities for the Number of Walks in Graphs","publication_year":2013,"publication_date":"2013-03-16","ids":{"openalex":"https://openalex.org/W2000198292","doi":"https://doi.org/10.1007/s00453-013-9766-3","mag":"2000198292"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-013-9766-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-013-9766-3","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://mediatum.ub.tum.de/node?id=1164662","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036701179","display_name":"Hanjo T\u00e4ubig","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Hanjo T\u00e4ubig","raw_affiliation_strings":["Institut f\u00fcr Informatik, TU M\u00fcnchen, Boltzmannstr. 3, 85748, Garching, Germany","Technische-Universit\u00e4t-M\u00fcnchen, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, TU M\u00fcnchen, Boltzmannstr. 3, 85748, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technische-Universit\u00e4t-M\u00fcnchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065895400","display_name":"Jeremias Weihmann","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Jeremias Weihmann","raw_affiliation_strings":["Institut f\u00fcr Informatik, TU M\u00fcnchen, Boltzmannstr. 3, 85748, Garching, Germany","Technische-Universit\u00e4t-M\u00fcnchen, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, TU M\u00fcnchen, Boltzmannstr. 3, 85748, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technische-Universit\u00e4t-M\u00fcnchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049639443","display_name":"Sven Kosub","orcid":"https://orcid.org/0000-0001-6316-8546"},"institutions":[{"id":"https://openalex.org/I189712700","display_name":"University of Konstanz","ror":"https://ror.org/0546hnb39","country_code":"DE","type":"education","lineage":["https://openalex.org/I189712700"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Sven Kosub","raw_affiliation_strings":["Fachbereich Informatik und Informationswissenschaft, Universit\u00e4t Konstanz, Fach 67, 78457, Konstanz, Germany","Universit\u00e4t Konstanz, Konstanz, Germany"],"affiliations":[{"raw_affiliation_string":"Fachbereich Informatik und Informationswissenschaft, Universit\u00e4t Konstanz, Fach 67, 78457, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]},{"raw_affiliation_string":"Universit\u00e4t Konstanz, Konstanz, Germany","institution_ids":["https://openalex.org/I189712700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058250506","display_name":"Raymond Hemmecke","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Raymond Hemmecke","raw_affiliation_strings":["Institut f\u00fcr Mathematik, TU M\u00fcnchen, Boltzmannstr. 3, 85748, Garching, Germany","Technische-Universit\u00e4t-M\u00fcnchen, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, TU M\u00fcnchen, Boltzmannstr. 3, 85748, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technische-Universit\u00e4t-M\u00fcnchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109876781","display_name":"Ernst Mayr","orcid":null},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ernst W. Mayr","raw_affiliation_strings":["Institut f\u00fcr Informatik, TU M\u00fcnchen, Boltzmannstr. 3, 85748, Garching, Germany","Technische-Universit\u00e4t-M\u00fcnchen, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, TU M\u00fcnchen, Boltzmannstr. 3, 85748, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"Technische-Universit\u00e4t-M\u00fcnchen, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5036701179"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":1.4125,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.79426386,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"66","issue":"4","first_page":"804","last_page":"828"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9990000128746033,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.998199999332428,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7895374298095703},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7452294826507568},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.6298344135284424},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5195717811584473},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5060359835624695},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.48824599385261536},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4749084711074829},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4638493061065674},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4467766284942627},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3896265923976898},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.37119895219802856},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1322784721851349},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08779850602149963}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7895374298095703},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7452294826507568},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.6298344135284424},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5195717811584473},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5060359835624695},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.48824599385261536},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4749084711074829},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4638493061065674},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4467766284942627},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3896265923976898},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.37119895219802856},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1322784721851349},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08779850602149963},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00453-013-9766-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00453-013-9766-3","pdf_url":null,"source":{"id":"https://openalex.org/S89324355","display_name":"Algorithmica","issn_l":"0178-4617","issn":["0178-4617","1432-0541"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1164662","is_oa":true,"landing_page_url":"http://mediatum.ub.tum.de/node?id=1164662","pdf_url":null,"source":{"id":"https://openalex.org/S4306400453","display_name":"mediaTUM \u2013 the media and publications repository of the Technical University Munich (Technical University Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:mediatum.ub.tum.de:node/1164662","is_oa":true,"landing_page_url":"http://mediatum.ub.tum.de/node?id=1164662","pdf_url":null,"source":{"id":"https://openalex.org/S4306400453","display_name":"mediaTUM \u2013 the media and publications repository of the Technical University Munich (Technical University Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"},"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":64,"referenced_works":["https://openalex.org/W88682288","https://openalex.org/W154962059","https://openalex.org/W610539324","https://openalex.org/W613836397","https://openalex.org/W960859969","https://openalex.org/W1559146381","https://openalex.org/W1567268701","https://openalex.org/W1578099820","https://openalex.org/W1589331344","https://openalex.org/W1595344052","https://openalex.org/W1608618407","https://openalex.org/W1966984493","https://openalex.org/W1977170634","https://openalex.org/W1985532698","https://openalex.org/W1986098644","https://openalex.org/W1989949971","https://openalex.org/W1990435776","https://openalex.org/W1992365495","https://openalex.org/W1996091068","https://openalex.org/W2000762131","https://openalex.org/W2003242355","https://openalex.org/W2010862576","https://openalex.org/W2014315572","https://openalex.org/W2014486909","https://openalex.org/W2023055866","https://openalex.org/W2028322627","https://openalex.org/W2036523948","https://openalex.org/W2036836182","https://openalex.org/W2039302045","https://openalex.org/W2046226064","https://openalex.org/W2052535020","https://openalex.org/W2055656009","https://openalex.org/W2064276984","https://openalex.org/W2071708841","https://openalex.org/W2074422414","https://openalex.org/W2075290268","https://openalex.org/W2079035824","https://openalex.org/W2079287570","https://openalex.org/W2090384185","https://openalex.org/W2110805362","https://openalex.org/W2112494680","https://openalex.org/W2131467982","https://openalex.org/W2143132812","https://openalex.org/W2154955356","https://openalex.org/W2155829240","https://openalex.org/W2164063505","https://openalex.org/W2279053140","https://openalex.org/W2317597502","https://openalex.org/W2327097903","https://openalex.org/W2330548796","https://openalex.org/W2737277256","https://openalex.org/W2747098299","https://openalex.org/W2782075917","https://openalex.org/W2963732942","https://openalex.org/W3127549917","https://openalex.org/W4210576943","https://openalex.org/W4210987083","https://openalex.org/W4213018468","https://openalex.org/W4241764762","https://openalex.org/W4247263392","https://openalex.org/W4251292291","https://openalex.org/W4254923354","https://openalex.org/W4255212053","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2077314575","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W4380682190","https://openalex.org/W2102386043","https://openalex.org/W2945307361","https://openalex.org/W2116636209","https://openalex.org/W2053698688","https://openalex.org/W2005710836","https://openalex.org/W4389599611"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}