{"id":"https://openalex.org/W2113569291","doi":"https://doi.org/10.37236/525","title":"Maximum Multiplicity of Matching Polynomial Roots and Minimum Path Cover in General Graphs","display_name":"Maximum Multiplicity of Matching Polynomial Roots and Minimum Path Cover in General Graphs","publication_year":2011,"publication_date":"2011-02-14","ids":{"openalex":"https://openalex.org/W2113569291","doi":"https://doi.org/10.37236/525","mag":"2113569291"},"language":"en","primary_location":{"id":"doi:10.37236/525","is_oa":true,"landing_page_url":"https://doi.org/10.37236/525","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p38/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/v18i1p38/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019759019","display_name":"Cheng Yeaw Ku","orcid":"https://orcid.org/0000-0002-8606-3402"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Cheng Yeaw Ku","raw_affiliation_strings":["National University of Singapore"],"affiliations":[{"raw_affiliation_string":"National University of Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069418477","display_name":"Kok Bin Wong","orcid":"https://orcid.org/0000-0001-5640-4432"},"institutions":[{"id":"https://openalex.org/I33849332","display_name":"University of Malaya","ror":"https://ror.org/00rzspn62","country_code":"MY","type":"education","lineage":["https://openalex.org/I33849332"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Kok Bin Wong","raw_affiliation_strings":["University of Malaya"],"affiliations":[{"raw_affiliation_string":"University of Malaya","institution_ids":["https://openalex.org/I33849332"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5019759019"],"corresponding_institution_ids":["https://openalex.org/I165932596"],"apc_list":null,"apc_paid":null,"fwci":1.479,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81836848,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9994000196456909,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9975000023841858,"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/mathematics","display_name":"Mathematics","score":0.8650964498519897},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8286299109458923},{"id":"https://openalex.org/keywords/multiplicity","display_name":"Multiplicity (mathematics)","score":0.7104827165603638},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.7068119645118713},{"id":"https://openalex.org/keywords/vertex-cover","display_name":"Vertex cover","score":0.5187525749206543},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.516265869140625},{"id":"https://openalex.org/keywords/edge-cover","display_name":"Edge cover","score":0.48617619276046753},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.4543936550617218},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45413076877593994},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.44572436809539795},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.440559059381485},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.40967071056365967},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.0691368579864502}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8650964498519897},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8286299109458923},{"id":"https://openalex.org/C156004811","wikidata":"https://www.wikidata.org/wiki/Q2228257","display_name":"Multiplicity (mathematics)","level":2,"score":0.7104827165603638},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.7068119645118713},{"id":"https://openalex.org/C40687702","wikidata":"https://www.wikidata.org/wiki/Q11515519","display_name":"Vertex cover","level":3,"score":0.5187525749206543},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.516265869140625},{"id":"https://openalex.org/C17762858","wikidata":"https://www.wikidata.org/wiki/Q594001","display_name":"Edge cover","level":3,"score":0.48617619276046753},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.4543936550617218},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45413076877593994},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44572436809539795},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.440559059381485},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.40967071056365967},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0691368579864502},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/525","is_oa":true,"landing_page_url":"https://doi.org/10.37236/525","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p38/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"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/103537","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/103537","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.37236/525","is_oa":true,"landing_page_url":"https://doi.org/10.37236/525","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p38/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":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2113569291.pdf","grobid_xml":"https://content.openalex.org/works/W2113569291.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1483244116","https://openalex.org/W1529283357","https://openalex.org/W1715502087","https://openalex.org/W2014552601","https://openalex.org/W2025871027","https://openalex.org/W2066456540","https://openalex.org/W4300568384"],"related_works":["https://openalex.org/W2036594069","https://openalex.org/W2156896570","https://openalex.org/W2949255922","https://openalex.org/W2038655901","https://openalex.org/W4241472005","https://openalex.org/W1627181101","https://openalex.org/W4244658307","https://openalex.org/W9203110","https://openalex.org/W2379188955","https://openalex.org/W2757966824"],"abstract_inverted_index":{"Let":[0],"$G$":[1],"be":[2,137],"a":[3,14,40,58,75,82,125],"graph.":[4,66],"It":[5],"is":[6,21,49,62,81],"well":[7],"known":[8],"that":[9,117],"the":[10,17,24,34,72,100,103,118,121,129],"maximum":[11,130],"multiplicity":[12,131],"of":[13,16,27,37,74,84,99,102,112,124,132],"root":[15,83],"matching":[18,133],"polynomial":[19,134],"$\\mu(G,x)$":[20],"at":[22],"most":[23],"minimum":[25,122],"number":[26],"vertex":[28,35],"disjoint":[29],"paths":[30],"needed":[31],"to":[32,92],"cover":[33,78,127],"set":[36],"$G$.":[38],"Recently,":[39],"necessary":[41],"and":[42,128],"sufficient":[43],"condition":[44],"for":[45,53,64,90,107],"which":[46,86],"this":[47,56],"bound":[48],"tight":[50],"was":[51,87],"found":[52],"trees.":[54],"In":[55],"paper,":[57],"similar":[59],"structural":[60],"characterization":[61],"proved":[63],"any":[65],"To":[67],"accomplish":[68],"this,":[69],"we":[70,114],"extend":[71],"notion":[73],"$(\\theta,G)$-extremal":[76],"path":[77,126],"(where":[79],"$\\theta$":[80],"$\\mu(G,x)$)":[85],"first":[88],"introduced":[89],"trees":[91],"general":[93,108],"graphs.":[94],"Our":[95],"proof":[96],"makes":[97],"use":[98],"analogue":[101],"Gallai-Edmonds":[104],"Structure":[105],"Theorem":[106],"root.":[109],"By":[110],"way":[111],"contrast,":[113],"also":[115],"show":[116],"difference":[119],"between":[120],"size":[123],"roots":[135],"can":[136],"arbitrarily":[138],"large.":[139]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
