{"id":"https://openalex.org/W4410466516","doi":"https://doi.org/10.1007/s00373-025-02930-9","title":"Recognizing Relating Edges in Graphs Without Cycles of Length 6","display_name":"Recognizing Relating Edges in Graphs Without Cycles of Length 6","publication_year":2025,"publication_date":"2025-05-17","ids":{"openalex":"https://openalex.org/W4410466516","doi":"https://doi.org/10.1007/s00373-025-02930-9"},"language":"en","primary_location":{"id":"doi:10.1007/s00373-025-02930-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02930-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02930-9.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"Graphs and Combinatorics","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/s00373-025-02930-9.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5085909262","display_name":"Vadim E. Levit","orcid":"https://orcid.org/0000-0002-4190-7050"},"institutions":[{"id":"https://openalex.org/I52170813","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97","country_code":"IL","type":"education","lineage":["https://openalex.org/I52170813"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Vadim E. Levit","raw_affiliation_strings":["Department of Mathematics, Ariel University, Ariel, Israel"],"raw_orcid":"https://orcid.org/0000-0002-4190-7050","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ariel University, Ariel, Israel","institution_ids":["https://openalex.org/I52170813"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030389852","display_name":"David Tankus","orcid":null},"institutions":[{"id":"https://openalex.org/I3129975082","display_name":"Sami Shamoon College of Engineering","ror":"https://ror.org/011aa4g29","country_code":"IL","type":"education","lineage":["https://openalex.org/I3129975082"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"David Tankus","raw_affiliation_strings":["Department of Software Engineering, Shamoon College of Engineering, Ashdod, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Software Engineering, Shamoon College of Engineering, Ashdod, Israel","institution_ids":["https://openalex.org/I3129975082"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5085909262"],"corresponding_institution_ids":["https://openalex.org/I52170813"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0836063,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9988999962806702,"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"}},{"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/T12541","display_name":"Graph Labeling and Dimension Problems","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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7536687254905701},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.720343291759491},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.35934966802597046}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7536687254905701},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.720343291759491},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35934966802597046}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00373-025-02930-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02930-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02930-9.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"Graphs and Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00373-025-02930-9","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00373-025-02930-9","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00373-025-02930-9.pdf","source":{"id":"https://openalex.org/S186126824","display_name":"Graphs and Combinatorics","issn_l":"0911-0119","issn":["0911-0119","1435-5914"],"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":"Graphs and Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320327767","display_name":"Ariel University","ror":"https://ror.org/03nz8qe97"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410466516.pdf","grobid_xml":"https://content.openalex.org/works/W4410466516.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1996466460","https://openalex.org/W1997658699","https://openalex.org/W2011039300","https://openalex.org/W2036243565","https://openalex.org/W2041022284","https://openalex.org/W2095895362","https://openalex.org/W2147078876","https://openalex.org/W2166890675","https://openalex.org/W2533671833","https://openalex.org/W2742680891","https://openalex.org/W2963412337","https://openalex.org/W2964077273","https://openalex.org/W3003815558","https://openalex.org/W3098601311","https://openalex.org/W4390955485","https://openalex.org/W4398241285","https://openalex.org/W4406651687"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"A":[1,195,229],"graph":[2,196],"G":[3,40,154,197,219],"is":[4,41,73,128,155,174,176,245,304,329,338],"well-covered":[5,44],"if":[6,45,75,211,247],"all":[7,46],"its":[8,47],"maximal":[9,48,123],"independent":[10,49,124,216,227,250],"sets":[11,50,217],"are":[12,51,122,160,220],"of":[13,52,161,192,347],"the":[14,53,200,314],"same":[15,54],"cardinality.":[16],"Let":[17],"$$w:V(G)":[18],"\\longrightarrow":[19],"\\mathbb":[20],"{R}$$":[21],"<mml:math":[22,61,81,98,112,133,204,234,257,278,294,318],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[23,62,82,99,113,134,205,235,258,279,295,319],"<mml:mrow>":[24,63,83,100,114,135,236,259,280,296],"<mml:mi>w</mml:mi>":[25,136,141],"<mml:mo>:</mml:mo>":[26],"<mml:mi>V</mml:mi>":[27,86,239,262],"<mml:mo>(</mml:mo>":[28,68,87,137,142,240,263,284],"<mml:mi>G</mml:mi>":[29,69,88,241,264],"<mml:mo>)</mml:mo>":[30,70,89,139,144,242,265,286],"<mml:mo>\u27f6</mml:mo>":[31],"<mml:mi>R</mml:mi>":[32],"</mml:mrow>":[33,71,90,106,120,145,243,271,287,302],"</mml:math>":[34,72,91,107,121,146,210,244,272,288,303,324],"be":[35],"a":[36],"weight":[37,149],"function.":[38],"Then":[39],"w":[42,151,156,166],"-":[43],"weight.":[55],"An":[56],"edge":[57,173],"$$xy":[58],"\\in":[59,232,276],"E(G)$$":[60],"<mml:mi>x</mml:mi>":[64,104,138],"<mml:mi>y</mml:mi>":[65,118,143],"<mml:mo>\u2208</mml:mo>":[66,238,282],"<mml:mi>E</mml:mi>":[67],"relating":[74,129,175],"there":[76,273],"exists":[77,274],"$$S":[78,95,109,252,291],"\\subseteq":[79,253],"V(G)$$":[80,233],"<mml:mi>S</mml:mi>":[84,101,115,260,297],"<mml:mo>\u2286</mml:mo>":[85,261],"such":[92,152,289],"that":[93,153,181,290,335],"both":[94],"\\cup":[96,110,292],"\\{x\\}$$":[97],"<mml:mo>\u222a</mml:mo>":[102,116,298],"<mml:mo>{</mml:mo>":[103,117,299],"<mml:mo>}</mml:mo>":[105,119,301],"and":[108],"\\{y\\}$$":[111],"sets.":[125,228],"If":[126],"xy":[127],"then":[130],"$$":[131],"w(x)=w(y)$$":[132],"<mml:mo>=</mml:mo>":[140],"for":[147,164,188,248,343],"every":[148,212,249],"function":[150],"-well-covered.":[157],"Relating":[158],"edges":[159],"crucial":[162],"importance":[163],"investigating":[165],"-well-covered":[167],"graphs.":[168],"The":[169],"problem":[170,183,337],"whether":[171],"an":[172,309],"NP-":[177,185,331,340],"complete.":[178,332],"We":[179,333],"prove":[180,334],"this":[182,336],"remains":[184],"complete":[186,341],"even":[187,342],"graphs":[189,344],"without":[190,345],"cycles":[191,346],"length":[193,348],"6.":[194,349],"belongs":[198],"to":[199],"class":[201,315],"$$\\mathbf":[202,316],"{W_{2}}$$":[203,317],"<mml:msub>":[206,320],"<mml:mi>W</mml:mi>":[207,321],"<mml:mn>2</mml:mn>":[208,322],"</mml:msub>":[209,323],"two":[213,223],"pairwise":[214,224],"disjoint":[215,225],"in":[218,222,312],"included":[221],"maximum":[226],"vertex":[230],"$$v":[231],"<mml:mi>v</mml:mi>":[237,269,285],"shedding":[246,327],"set":[251],"V(G)":[254],"\\setminus":[255],"N[v]$$":[256],"<mml:mo>\\</mml:mo>":[266],"<mml:mi>N</mml:mi>":[267,283],"<mml:mo>[</mml:mo>":[268],"<mml:mo>]</mml:mo>":[270],"$$u":[275],"N(v)$$":[277],"<mml:mi>u</mml:mi>":[281,300],"\\{u\\}$$":[293],"independent.":[305],"Shedding":[306],"vertices":[307,328],"play":[308],"important":[310],"role":[311],"studying":[313],".":[325],"Recognizing":[326],"co-":[330,339]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}