{"id":"https://openalex.org/W4410207421","doi":"https://doi.org/10.1007/s00453-025-01318-8","title":"Matching Cuts in Graphs of High Girth and H-Free Graphs","display_name":"Matching Cuts in Graphs of High Girth and H-Free Graphs","publication_year":2025,"publication_date":"2025-05-08","ids":{"openalex":"https://openalex.org/W4410207421","doi":"https://doi.org/10.1007/s00453-025-01318-8"},"language":"en","primary_location":{"id":"doi:10.1007/s00453-025-01318-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-025-01318-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-025-01318-8.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00453-025-01318-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064429511","display_name":"Carl Feghali","orcid":"https://orcid.org/0000-0001-6727-7213"},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Carl Feghali","raw_affiliation_strings":["University of Lyon, EnsL, CNRS, LIP, 69342, Lyon Cedex 07, France"],"raw_orcid":"https://orcid.org/0000-0001-6727-7213","affiliations":[{"raw_affiliation_string":"University of Lyon, EnsL, CNRS, LIP, 69342, Lyon Cedex 07, France","institution_ids":["https://openalex.org/I113428412","https://openalex.org/I100532134","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045385502","display_name":"Felicia Lucke","orcid":"https://orcid.org/0000-0002-9860-2928"},"institutions":[{"id":"https://openalex.org/I154338468","display_name":"University of Fribourg","ror":"https://ror.org/022fs9h90","country_code":"CH","type":"education","lineage":["https://openalex.org/I154338468"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Felicia Lucke","raw_affiliation_strings":["Department of Informatics, University of Fribourg, Fribourg, Switzerland"],"raw_orcid":"https://orcid.org/0000-0002-9860-2928","affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Fribourg, Fribourg, Switzerland","institution_ids":["https://openalex.org/I154338468"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027487467","display_name":"Dani\u00ebl Paulusma","orcid":"https://orcid.org/0000-0001-5945-9287"},"institutions":[{"id":"https://openalex.org/I190082696","display_name":"Durham University","ror":"https://ror.org/01v29qb04","country_code":"GB","type":"education","lineage":["https://openalex.org/I190082696"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Dani\u00ebl Paulusma","raw_affiliation_strings":["Department of Computer Science, Durham University, Durham, UK"],"raw_orcid":"https://orcid.org/0000-0001-5945-9287","affiliations":[{"raw_affiliation_string":"Department of Computer Science, Durham University, Durham, UK","institution_ids":["https://openalex.org/I190082696"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5040690366","display_name":"Bernard Ries","orcid":"https://orcid.org/0000-0003-4395-5547"},"institutions":[{"id":"https://openalex.org/I154338468","display_name":"University of Fribourg","ror":"https://ror.org/022fs9h90","country_code":"CH","type":"education","lineage":["https://openalex.org/I154338468"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Bernard Ries","raw_affiliation_strings":["Department of Informatics, University of Fribourg, Fribourg, Switzerland"],"raw_orcid":"https://orcid.org/0000-0003-4395-5547","affiliations":[{"raw_affiliation_string":"Department of Informatics, University of Fribourg, Fribourg, Switzerland","institution_ids":["https://openalex.org/I154338468"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5064429511"],"corresponding_institution_ids":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":5.0803,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.95199775,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"87","issue":"8","first_page":"1199","last_page":"1221"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":1.0,"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":1.0,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998000264167786,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9966999888420105,"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/combinatorics","display_name":"Combinatorics","score":0.7379602193832397},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6135172247886658},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6034250855445862},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.5658857226371765},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.542661190032959},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.44394975900650024},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.44292449951171875},{"id":"https://openalex.org/keywords/odd-graph","display_name":"Odd graph","score":0.4208664298057556},{"id":"https://openalex.org/keywords/indifference-graph","display_name":"Indifference graph","score":0.4129217267036438},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.2919606864452362},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.24376127123832703},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12410286068916321}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7379602193832397},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6135172247886658},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6034250855445862},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.5658857226371765},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.542661190032959},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44394975900650024},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.44292449951171875},{"id":"https://openalex.org/C206815938","wikidata":"https://www.wikidata.org/wiki/Q7077445","display_name":"Odd graph","level":5,"score":0.4208664298057556},{"id":"https://openalex.org/C74133993","wikidata":"https://www.wikidata.org/wiki/Q3115472","display_name":"Indifference graph","level":3,"score":0.4129217267036438},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.2919606864452362},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.24376127123832703},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12410286068916321},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00453-025-01318-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-025-01318-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-025-01318-8.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-05368784v1","is_oa":false,"landing_page_url":"https://hal.science/hal-05368784","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithmica, 2025, 87 (8), pp.1199-1221. &#x27E8;10.1007/s00453-025-01318-8&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:freidok.uni-freiburg.de:279994","is_oa":false,"landing_page_url":"https://freidok.uni-freiburg.de/data/279994","pdf_url":null,"source":{"id":"https://openalex.org/S4306401057","display_name":"FreiDok plus (Universit\u00e4tsbibliothek Freiburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161046081","host_organization_name":"University of Freiburg","host_organization_lineage":["https://openalex.org/I161046081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithmica. - 87, 8 (2025) , 1199-1221, ISSN: 1432-0541","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00453-025-01318-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00453-025-01318-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00453-025-01318-8.pdf","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithmica","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323471","display_name":"Universit\u00e9 de Fribourg","ror":"https://ror.org/022fs9h90"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410207421.pdf","grobid_xml":"https://content.openalex.org/works/W4410207421.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1986824573","https://openalex.org/W1993111701","https://openalex.org/W1997541985","https://openalex.org/W2038098381","https://openalex.org/W2046680668","https://openalex.org/W2056827961","https://openalex.org/W2082548475","https://openalex.org/W2087872235","https://openalex.org/W2153737011","https://openalex.org/W2173904855","https://openalex.org/W2190210389","https://openalex.org/W2738197751","https://openalex.org/W2798321768","https://openalex.org/W2998596251","https://openalex.org/W3110459966","https://openalex.org/W3131349932","https://openalex.org/W3166674481","https://openalex.org/W3184379502","https://openalex.org/W3187874026","https://openalex.org/W4235946010","https://openalex.org/W4282919382","https://openalex.org/W4296666778","https://openalex.org/W4386974052","https://openalex.org/W4394679376","https://openalex.org/W6600158986"],"related_works":["https://openalex.org/W2157783000","https://openalex.org/W4287117052","https://openalex.org/W4206705200","https://openalex.org/W2966902162","https://openalex.org/W1893557706","https://openalex.org/W4214565117","https://openalex.org/W2407722793","https://openalex.org/W2028363955","https://openalex.org/W2008957319","https://openalex.org/W2075191511"],"abstract_inverted_index":{"Abstract":[0],"The":[1,23],"(Perfect)":[2],"Matching":[3,26,45,50,61,81,86,105,156,160,165,212,241],"Cut":[4,46,62,82,106,157,161,213,242],"problem":[5,27,120],"is":[6,18,28,63,138,216,257],"to":[7,29,65,217],"decide":[8,30],"if":[9,31],"a":[10,14,32,36,41,108,175,204,219,224,235],"connected":[11,33,176],"graph":[12,34,225],"has":[13,35],"(perfect)":[15],"matching":[16,38,42,221],"that":[17,39,80,116,155],"also":[19,88,114],"an":[20],"edge":[21],"cut.":[22,43],"Disconnected":[24,48,84,163],"Perfect":[25,49,60,85,159,164,240],"perfect":[37],"contains":[40,174],"Both":[44],"and":[47,83,98,148,162,196,202,206],"are":[51,87,166],"-complete":[52,67,89,139,167],"for":[53,69,90,104,124,140,168,192,243],"planar":[54],"graphs":[55,72,92,142,171,195,250],"of":[56,73,93,143,181,209,223,239,261],"girth":[57,97,147],"5,":[58],"whereas":[59],"known":[64,205],"be":[66],"even":[68],"subcubic":[70],"bipartite":[71,91,141],"arbitrarily":[74,94,144],"large":[75,95,145],"fixed":[76,96,126,146],"girth.":[77],"We":[78,113],"prove":[79],"bounded":[99,149],"maximum":[100,150],"degree.":[101,151],"Our":[102],"result":[103],"resolves":[107],"20-year":[109],"old":[110],"open":[111],"problem.":[112],"show":[115,154],"the":[117,189,210],"more":[118],"general":[119],"d":[121],"-Cut":[122],",":[123,137,158],"every":[125],"$$d\\ge":[127],"1$$":[128],"<mml:math":[129,245,253],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[130,246,254],"<mml:mrow>":[131],"<mml:mi>d</mml:mi>":[132],"<mml:mo>\u2265</mml:mo>":[133],"<mml:mn>1</mml:mn>":[134],"</mml:mrow>":[135],"</mml:math>":[136,248,256],"Furthermore,":[152],"we":[153,187,233],"H":[169,173,193],"-free":[170,194],"whenever":[172],"component":[177],"with":[178,199,203],"two":[179],"vertices":[180],"degree":[182],"at":[183],"least":[184],"3.":[185],"Afterwards,":[186],"update":[188],"state-of-the-art":[190],"summaries":[191],"compare":[197],"them":[198],"each":[200],"other,":[201],"full":[207],"classification":[208,238],"Maximum":[211],"problem,":[214],"which":[215],"determine":[218],"largest":[220],"cut":[222],"G":[226],".":[227],"Finally,":[228],"by":[229],"combining":[230],"existing":[231],"results,":[232],"obtain":[234],"complete":[236],"complexity":[237],"$$\\mathcal{H}$$":[244,252],"<mml:mi>H</mml:mi>":[247,255],"-subgraph-free":[249],"where":[251],"any":[258],"finite":[259],"set":[260],"graphs.":[262]},"counts_by_year":[{"year":2025,"cited_by_count":4}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
