{"id":"https://openalex.org/W2962956566","doi":"https://doi.org/10.37236/7109","title":"On Vertex-Disjoint Paths in Regular Graphs","display_name":"On Vertex-Disjoint Paths in Regular Graphs","publication_year":2018,"publication_date":"2018-04-27","ids":{"openalex":"https://openalex.org/W2962956566","doi":"https://doi.org/10.37236/7109","mag":"2962956566"},"language":"en","primary_location":{"id":"doi:10.37236/7109","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7109","pdf_url":null,"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://doi.org/10.37236/7109","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086267413","display_name":"Jie Han","orcid":"https://orcid.org/0000-0002-2013-2962"},"institutions":[{"id":"https://openalex.org/I17974374","display_name":"Universidade de S\u00e3o Paulo","ror":"https://ror.org/036rp1748","country_code":"BR","type":"education","lineage":["https://openalex.org/I17974374"]}],"countries":["BR"],"is_corresponding":true,"raw_author_name":"Jie Han","raw_affiliation_strings":["Universidade de S\u00e3o Paulo"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade de S\u00e3o Paulo","institution_ids":["https://openalex.org/I17974374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086267413"],"corresponding_institution_ids":["https://openalex.org/I17974374"],"apc_list":null,"apc_paid":null,"fwci":1.6076,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.82651391,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"25","issue":"2","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":0.9988999962806702,"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":0.9988999962806702,"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":0.9987999796867371,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9966999888420105,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8846466541290283},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8383883237838745},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.6775959134101868},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6152122616767883},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5127357244491577},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4587249457836151},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4539882242679596},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45053407549858093},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4246654808521271},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.060908615589141846}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8846466541290283},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8383883237838745},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.6775959134101868},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6152122616767883},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5127357244491577},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4587249457836151},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4539882242679596},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45053407549858093},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4246654808521271},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.060908615589141846},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/7109","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7109","pdf_url":null,"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:10.37236/7109","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7109","pdf_url":null,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2371352078","https://openalex.org/W2953461625","https://openalex.org/W2077383796","https://openalex.org/W1971174658","https://openalex.org/W2080136900","https://openalex.org/W2099195351","https://openalex.org/W2372768926","https://openalex.org/W2478481870","https://openalex.org/W2072510267","https://openalex.org/W3031681467"],"abstract_inverted_index":{"Let":[0],"$c\\in":[1],"(0,":[2],"1]$":[3],"be":[4,11,73],"a":[5,12,26],"real":[6],"number":[7,69],"and":[8,55],"let":[9],"$n$":[10],"sufficiently":[13],"large":[14],"integer.":[15],"We":[16],"prove":[17],"that":[18],"every":[19],"$n$-vertex":[20],"$c":[21],"n$-regular":[22],"graph":[23],"$G$":[24,64],"contains":[25],"collection":[27],"of":[28,42,70],"$\\lfloor":[29,46,76],"1/c":[30,47],"\\rfloor$":[31,48],"paths":[32,71],"whose":[33],"union":[34],"covers":[35],"all":[36],"but":[37],"at":[38],"most":[39],"$o(n)$":[40],"vertices":[41],"$G$.":[43],"The":[44],"constant":[45],"is":[49,65,80],"best":[50,81],"possible":[51],"when":[52],"$1/c\\notin":[53],"\\mathbb{N}$":[54],"off":[56],"by":[57],"$1$":[58],"otherwise.":[59],"Moreover,":[60],"if":[61],"in":[62],"addition":[63],"bipartite,":[66],"then":[67],"the":[68],"can":[72],"reduced":[74],"to":[75],"1/(2c)":[77],"\\rfloor$,":[78],"which":[79],"possible.":[82]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
