{"id":"https://openalex.org/W4362699352","doi":"https://doi.org/10.37236/11141","title":"Enumeration of Perfect Matchings of the Cartesian Products of Graphs","display_name":"Enumeration of Perfect Matchings of the Cartesian Products of Graphs","publication_year":2023,"publication_date":"2023-04-07","ids":{"openalex":"https://openalex.org/W4362699352","doi":"https://doi.org/10.37236/11141"},"language":"en","primary_location":{"id":"doi:10.37236/11141","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11141","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p2/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p2/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100318309","display_name":"Wei Li","orcid":"https://orcid.org/0000-0002-9057-0570"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Li","raw_affiliation_strings":["Northwestern Polytechnical University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Northwestern Polytechnical University","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100318971","display_name":"Yao Wang","orcid":"https://orcid.org/0000-0002-1064-7946"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yao Wang","raw_affiliation_strings":["School of Computer Science Northwestern Polytechnical University Xi'an, Shaanxi 710129, China","School of Mathematics and Statistics Northwestern Polytechnical University Xi'an, Shaanxi 710129, China","Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen, Guangdong 518057, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Computer Science Northwestern Polytechnical University Xi'an, Shaanxi 710129, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"School of Mathematics and Statistics Northwestern Polytechnical University Xi'an, Shaanxi 710129, China","institution_ids":["https://openalex.org/I17145004"]},{"raw_affiliation_string":"Research & Development Institute of Northwestern Polytechnical University in Shenzhen, Shenzhen, Guangdong 518057, China","institution_ids":["https://openalex.org/I17145004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I17145004"],"apc_list":null,"apc_paid":null,"fwci":0.1439,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.44056343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"30","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","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"}},{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9988999962806702,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9987000226974487,"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":0.8842554092407227},{"id":"https://openalex.org/keywords/pfaffian","display_name":"Pfaffian","score":0.8167480230331421},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7936848402023315},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5214190483093262},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4662664532661438},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.445709764957428}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8842554092407227},{"id":"https://openalex.org/C2775956649","wikidata":"https://www.wikidata.org/wiki/Q1189744","display_name":"Pfaffian","level":2,"score":0.8167480230331421},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7936848402023315},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5214190483093262},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4662664532661438},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.445709764957428}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/11141","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11141","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p2/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"}],"best_oa_location":{"id":"doi:10.37236/11141","is_oa":true,"landing_page_url":"https://doi.org/10.37236/11141","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v30i2p2/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":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320336567","display_name":"Natural Science Basic Research Program of Shaanxi Province","ror":null},{"id":"https://openalex.org/F4320337111","display_name":"Basic and Applied Basic Research Foundation of Guangdong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4362699352.pdf"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W415832010","https://openalex.org/W1493587381","https://openalex.org/W1970687036","https://openalex.org/W1978655847","https://openalex.org/W1982250981","https://openalex.org/W1995353327","https://openalex.org/W1998417100","https://openalex.org/W2006912660","https://openalex.org/W2031024136","https://openalex.org/W2048821669","https://openalex.org/W2051271137","https://openalex.org/W2064153357","https://openalex.org/W2064675298","https://openalex.org/W2094655176","https://openalex.org/W2099198013","https://openalex.org/W2104165848","https://openalex.org/W2134417698","https://openalex.org/W2842463731","https://openalex.org/W2952214352","https://openalex.org/W4206603976","https://openalex.org/W6642990227","https://openalex.org/W6675486728","https://openalex.org/W6680804297"],"related_works":["https://openalex.org/W3086542228","https://openalex.org/W2000008285","https://openalex.org/W4286978554","https://openalex.org/W2989925696","https://openalex.org/W4297730031","https://openalex.org/W2471372608","https://openalex.org/W782850337","https://openalex.org/W2963365621","https://openalex.org/W3205099810","https://openalex.org/W2158949528"],"abstract_inverted_index":{"A":[0],"subgraph":[1],"$":[2,4,12,14,22,24,41,58,60,64,66,80,82,87,91,93,98,100,108,137,141,171,175],"H":[3],"of":[5,36,38,46,48,61,71,79,118,121,148,204,207,216,219,223,231,241],"a":[6,16,62,95,179],"graph":[7,28,63,104,136,170,210,222,234],"$G$":[8,177,191],"is":[9,29,54,73,83,163,178],"nice":[10,77],"if":[11,32,75],"G-V(H)":[13],"has":[15],"perfect":[17,205,229],"matching.":[18],"An":[19,56],"even":[20,69],"cycle":[21,78],"C":[23,42],"in":[25,86,214],"an":[26,68],"oriented":[27,31,85],"oddly":[30,84],"for":[33],"either":[34],"choice":[35],"direction":[37],"traversal":[39,53],"around":[40],"$,":[43],"the":[44,52,134,145,168,188,189,202,208,217,220,239],"number":[45,70,203],"edges":[47],"$C$":[49],"directed":[50],"along":[51],"odd.":[55],"orientation":[57,221],"D":[59,88],"G":[65,81,138,172],"with":[67,142],"vertices":[72],"Pfaffian":[74,103,116,135,169,209,233],"every":[76],"$.":[89],"Let":[90],"P_{n}":[92],"denote":[94],"path":[96],"on":[97],"n":[99],"vertices.":[101],"The":[102],"$G":[105,211,235],"\\times":[106,139,173,212,236],"P_{2n}":[107],"was":[109],"determined":[110],"by":[111,238],"Lu":[112],"and":[113,154,182,225],"Zhang":[114],"[The":[115],"property":[117],"Cartesian":[119],"products":[120],"graphs,":[122],"J.":[123],"Comb.":[124],"Optim.":[125],"27":[126],"(2014)":[127],"530--540].":[128],"In":[129],"this":[130,185],"paper,":[131],"we":[132,166,183,200,226],"characterize":[133,167],"P_{2n+1}":[140],"respect":[143],"to":[144,187],"forbidden":[146],"subgraphs":[147],"$G$.":[149,242],"We":[150],"first":[151],"give":[152],"sufficient":[153],"necessary":[155],"conditions":[156],"under":[157],"which":[158],"$G\\times":[159],"P_{2n+1}$":[160],"($n\\geqslant":[161],"2$)":[162],"Pfaffian.":[164],"Then":[165],"P_{3}":[174],"when":[176],"bipartite":[180],"graph,":[181],"generalize":[184],"result":[186],"case":[190],"contains":[192],"exactly":[193],"one":[194],"odd":[195],"cycle.":[196],"Following":[197],"these":[198],"results,":[199],"enumerate":[201],"matchings":[206,230],"P_{n}$":[213,237],"terms":[215],"eigenvalues":[218,240],"$G$,":[224],"also":[227],"count":[228],"some":[232]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}