{"id":"https://openalex.org/W2905023271","doi":"https://doi.org/10.1090/mcom/3465","title":"Graphs with few hamiltonian cycles","display_name":"Graphs with few hamiltonian cycles","publication_year":2019,"publication_date":"2019-06-12","ids":{"openalex":"https://openalex.org/W2905023271","doi":"https://doi.org/10.1090/mcom/3465","mag":"2905023271"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3465","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3465","pdf_url":"https://www.ams.org/mcom/2020-89-322/S0025-5718-2019-03465-8/S0025-5718-2019-03465-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2020-89-322/S0025-5718-2019-03465-8/S0025-5718-2019-03465-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057847156","display_name":"Jan Goedgebeur","orcid":"https://orcid.org/0000-0001-8984-2463"},"institutions":[{"id":"https://openalex.org/I130929987","display_name":"University of Mons","ror":"https://ror.org/02qnnz951","country_code":"BE","type":"education","lineage":["https://openalex.org/I130929987"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Jan Goedgebeur","raw_affiliation_strings":["Department of Applied Mathematics, Computer Science & Statistics, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium; and Computer Science Department, University of Mons, Place du Parc 20, 7000 Mons, Belgium","Computer Science Department, University of Mons, Place du Parc 20, 7000 Mons, Belgium","Department of Applied Mathematics, Computer Science & Statistics, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Computer Science & Statistics, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium; and Computer Science Department, University of Mons, Place du Parc 20, 7000 Mons, Belgium","institution_ids":["https://openalex.org/I130929987","https://openalex.org/I32597200"]},{"raw_affiliation_string":"Computer Science Department, University of Mons, Place du Parc 20, 7000 Mons, Belgium","institution_ids":["https://openalex.org/I130929987"]},{"raw_affiliation_string":"Department of Applied Mathematics, Computer Science & Statistics, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062754481","display_name":"Barbara Meersman","orcid":null},"institutions":[{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Barbara Meersman","raw_affiliation_strings":["Department of Applied Mathematics, Computer Science & Statistics, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Computer Science & Statistics, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031033019","display_name":"Carol T. Zamfirescu","orcid":"https://orcid.org/0000-0002-9673-410X"},"institutions":[{"id":"https://openalex.org/I3125347698","display_name":"Babe\u0219-Bolyai University","ror":"https://ror.org/02rmd1t30","country_code":"RO","type":"education","lineage":["https://openalex.org/I3125347698"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE","RO"],"is_corresponding":false,"raw_author_name":"Carol Zamfirescu","raw_affiliation_strings":["Department of Applied Mathematics, Computer Science & Statistics, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium; and Department of Mathematics, Babe\u00c5\u009f-Bolyai University, Cluj-Napoca, Roumania","Department of Applied Mathematics, Computer Science & Statistics, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium","Department of Mathematics, Babe\u015f-Bolyai University, Cluj-Napoca, Roumania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Computer Science & Statistics, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium; and Department of Mathematics, Babe\u00c5\u009f-Bolyai University, Cluj-Napoca, Roumania","institution_ids":["https://openalex.org/I32597200","https://openalex.org/I3125347698"]},{"raw_affiliation_string":"Department of Applied Mathematics, Computer Science & Statistics, Ghent University, Krijgslaan 281-S9, 9000 Ghent, Belgium","institution_ids":["https://openalex.org/I32597200"]},{"raw_affiliation_string":"Department of Mathematics, Babe\u015f-Bolyai University, Cluj-Napoca, Roumania","institution_ids":["https://openalex.org/I3125347698"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8193,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.86215066,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"89","issue":"322","first_page":"965","last_page":"991"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9983000159263611,"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/conjecture","display_name":"Conjecture","score":0.8237571716308594},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.8039343357086182},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8020163774490356},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6987324953079224},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6914544105529785},{"id":"https://openalex.org/keywords/cubic-graph","display_name":"Cubic graph","score":0.5964496731758118},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.5347040891647339},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.481889545917511},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4555470049381256},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39930257201194763},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.17353641986846924},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10900193452835083}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8237571716308594},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.8039343357086182},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8020163774490356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6987324953079224},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6914544105529785},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.5964496731758118},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.5347040891647339},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.481889545917511},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4555470049381256},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39930257201194763},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.17353641986846924},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10900193452835083},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.0},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1090/mcom/3465","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3465","pdf_url":"https://www.ams.org/mcom/2020-89-322/S0025-5718-2019-03465-8/S0025-5718-2019-03465-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/681502","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/681502","pdf_url":null,"source":{"id":"https://openalex.org/S7407055369","display_name":"Lirias","issn_l":null,"issn":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Mathematics Of Computation, vol. 89 (322), (965-991)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1812.05650","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1812.05650","pdf_url":"https://arxiv.org/pdf/1812.05650","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:archive.ugent.be:8644517","is_oa":false,"landing_page_url":"http://hdl.handle.net/1854/LU-8644517","pdf_url":null,"source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1088-6842","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:orbi.umons.ac.be:20.500.12907/10982","is_oa":false,"landing_page_url":"https://orbi.umons.ac.be/handle/20.500.12907/10982","pdf_url":null,"source":{"id":"https://openalex.org/S7407055454","display_name":"ORBi UMONS","issn_l":null,"issn":null,"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":"Mathematics of Computation, 89, 965-991 (2020-01-15)","raw_type":"peer reviewed"},{"id":"pmh:oai:orbi.umons.ac.be:20.500.12907/7587","is_oa":false,"landing_page_url":"https://orbi.umons.ac.be/handle/20.500.12907/7587","pdf_url":null,"source":{"id":"https://openalex.org/S7407055454","display_name":"ORBi UMONS","issn_l":null,"issn":null,"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":"9th Slovenian International Conference on Graph Theory, Bled, Slovenia [SI], 2019","raw_type":"info:eu-repo/semantics/conferencePaper"}],"best_oa_location":{"id":"doi:10.1090/mcom/3465","is_oa":true,"landing_page_url":"https://doi.org/10.1090/mcom/3465","pdf_url":"https://www.ams.org/mcom/2020-89-322/S0025-5718-2019-03465-8/S0025-5718-2019-03465-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Life below water","id":"https://metadata.un.org/sdg/14"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320322603","display_name":"Universiteit Gent","ror":"https://ror.org/00cv9y106"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2905023271.pdf","grobid_xml":"https://content.openalex.org/works/W2905023271.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W67348729","https://openalex.org/W1504855246","https://openalex.org/W1530753374","https://openalex.org/W1564921898","https://openalex.org/W1983648682","https://openalex.org/W1990600049","https://openalex.org/W1992797912","https://openalex.org/W1994661668","https://openalex.org/W1995621089","https://openalex.org/W1999227640","https://openalex.org/W2007351870","https://openalex.org/W2028767175","https://openalex.org/W2033296948","https://openalex.org/W2046452920","https://openalex.org/W2047039514","https://openalex.org/W2066542589","https://openalex.org/W2080276486","https://openalex.org/W2088096994","https://openalex.org/W2104180013","https://openalex.org/W2121655825","https://openalex.org/W2126209209","https://openalex.org/W2131754869","https://openalex.org/W2138867415","https://openalex.org/W2219797017","https://openalex.org/W2335389215","https://openalex.org/W2407557179","https://openalex.org/W2490772428","https://openalex.org/W2510299347","https://openalex.org/W2753005921","https://openalex.org/W2784050131","https://openalex.org/W2966470250","https://openalex.org/W4241301040","https://openalex.org/W4253659528","https://openalex.org/W4285719527","https://openalex.org/W6685003369","https://openalex.org/W6697766414"],"related_works":["https://openalex.org/W2963537714","https://openalex.org/W2886427884","https://openalex.org/W2620499272","https://openalex.org/W4298439799","https://openalex.org/W1541834747","https://openalex.org/W2074335998","https://openalex.org/W2761007407","https://openalex.org/W4299367522","https://openalex.org/W2066230947","https://openalex.org/W2508797883"],"abstract_inverted_index":{"We":[0,173,210,249,282],"describe":[1,272],"an":[2,236],"algorithm":[3,66],"for":[4,44,275,360],"the":[5,151,178,256,348,376],"exhaustive":[6],"generation":[7],"of":[8,37,64,94,99,110,154,157,167,177,180,192,218,258,269,331,338,343,351,379,397],"non-isomorphic":[9],"graphs":[10,76,109,280,321,342,352,381],"with":[11,70,322],"a":[12,91,155,165,308,329],"given":[13],"number":[14,378],"<inline-formula":[15,46,112,125,223,287,363,383],"content-type=\"math/mathml\">":[16,47,113,126,224,288,364,384],"<mml:math":[17,48,114,127,225,289,365,385],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[18,49,115,128,226,290,366,386],"alttext=\"k":[19],"greater-than-or-equal-to":[20,130],"0\">":[21],"<mml:semantics>":[22,51,117,132,228,292,368,388],"<mml:mrow>":[23,133],"<mml:mi>k</mml:mi>":[24,52],"<mml:mo>":[25,135],"\u2265":[26,136],"</mml:mo>":[27,137],"<mml:mn>0</mml:mn>":[28],"</mml:mrow>":[29,139],"<mml:annotation":[30,53,119,140,230,294,370,390],"encoding=\"application/x-tex\">k":[31],"\\ge":[32,142],"0</mml:annotation>":[33],"</mml:semantics>":[34,55,121,144,232,296,372,392],"</mml:math>":[35,56,122,145,233,297,373,393],"</inline-formula>":[36,57,123,146,234,298,374,394],"hamiltonian":[38,80,86,216,247,325,356],"cycles,":[39,326],"which":[40,276],"is":[41,147,262],"especially":[42],"efficient":[43],"small":[45],"alttext=\"k\">":[50],"encoding=\"application/x-tex\">k</mml:annotation>":[54],".":[58],"Our":[59],"main":[60],"findings,":[61],"combining":[62],"applications":[63],"this":[65],"and":[67,96,159,161,182,201,243,310,333,358,396],"existing":[68],"algorithms":[69],"new":[71],"theoretical":[72],"results,":[73],"revolve":[74],"around":[75],"containing":[77,353],"exactly":[78,84,323,354],"one":[79,355],"cycle":[81],"(1H)":[82],"or":[83],"three":[85],"cycles":[87],"(3H).":[88],"Motivated":[89],"by":[90,171],"classic":[92],"result":[93],"Smith":[95],"recent":[97],"work":[98,268,337],"Royle,":[100],"we":[101,271,346],"show":[102,202,311],"that":[103,184,203,214,239,260,301,312],"there":[104,261,313],"exist":[105,314],"nearly":[106],"cubic":[107,277,304,320],"1H":[108,187,265,341],"order":[111,199,254,286,362],"alttext=\"n\">":[116,367,387],"<mml:mi>n</mml:mi>":[118,134,369,389],"encoding=\"application/x-tex\">n</mml:annotation>":[120,371,391],"iff":[124],"alttext=\"n":[129],"18\">":[131],"<mml:mn>18</mml:mn>":[138],"encoding=\"application/x-tex\">n":[141],"18</mml:annotation>":[143],"even.":[148],"This":[149],"gives":[150],"strongest":[152],"form":[153],"theorem":[156],"Entringer":[158],"Swart,":[160],"sheds":[162],"light":[163],"on":[164,340,382],"question":[166,330],"Fleischner":[168],"originally":[169],"settled":[170],"Seamone.":[172],"prove":[174],"equivalent":[175],"formulations":[176],"conjecture":[179,213,257,300],"Bondy":[181],"Jackson":[183],"every":[185,215,302,361],"planar":[186,303,317],"graph":[188,217,306],"contains":[189,235,307],"two":[190],"vertices":[191,395],"degree":[193,220],"2,":[194],"verify":[195,251,283],"it":[196],"up":[197,252,284],"to":[198,253,285],"16,":[200],"its":[204,241,244],"toric":[205],"analogue":[206],"does":[207],"not":[208],"hold.":[209],"treat":[211],"Thomassen\u2019s":[212],"minimum":[219],"at":[221],"least":[222],"alttext=\"3\">":[227],"<mml:mn>3</mml:mn>":[229],"encoding=\"application/x-tex\">3</mml:annotation>":[231],"edge":[237],"such":[238,380],"both":[240],"removal":[242],"contraction":[245],"yield":[246],"graphs.":[248],"also":[250],"21":[255],"Sheehan":[259,339],"no":[263],"4-regular":[264],"graph.":[266],"Extending":[267],"Schwenk,":[270],"all":[273],"orders":[274],"3H":[278,305],"triangle-free":[279],"exist.":[281],"alttext=\"48\">":[291],"<mml:mn>48</mml:mn>":[293],"encoding=\"application/x-tex\">48</mml:annotation>":[295],"Cantoni\u2019s":[299],"triangle,":[309],"infinitely":[315],"many":[316],"cyclically":[318],"4-edge-connected":[319],"four":[324],"thereby":[327],"answering":[328],"Chia":[332],"Thomassen.":[334],"Finally,":[335],"complementing":[336],"maximum":[344,349,398],"size,":[345],"determine":[347],"size":[350],"path":[357],"give,":[359],",":[375],"exact":[377],"size.":[399]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}