{"id":"https://openalex.org/W3000716540","doi":"https://doi.org/10.37236/936","title":"Constructing Hypohamiltonian Snarks with Cyclic Connectivity $5$ and $6$","display_name":"Constructing Hypohamiltonian Snarks with Cyclic Connectivity $5$ and $6$","publication_year":2007,"publication_date":"2007-01-29","ids":{"openalex":"https://openalex.org/W3000716540","doi":"https://doi.org/10.37236/936","mag":"3000716540"},"language":"en","primary_location":{"id":"doi:10.37236/936","is_oa":true,"landing_page_url":"https://doi.org/10.37236/936","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r18/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/v14i1r18/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038322764","display_name":"Edita M\u00e1\u010dajov\u00e1","orcid":"https://orcid.org/0000-0001-5735-5513"},"institutions":[{"id":"https://openalex.org/I74788687","display_name":"Comenius University Bratislava","ror":"https://ror.org/0587ef340","country_code":"SK","type":"education","lineage":["https://openalex.org/I74788687"]}],"countries":["SK"],"is_corresponding":true,"raw_author_name":"Edita M\u00e1\u010dajov\u00e1","raw_affiliation_strings":["Department of Computer Science Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovakia"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovakia","institution_ids":["https://openalex.org/I74788687"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033117907","display_name":"Martin \u0160koviera","orcid":"https://orcid.org/0000-0002-2108-7518"},"institutions":[{"id":"https://openalex.org/I74788687","display_name":"Comenius University Bratislava","ror":"https://ror.org/0587ef340","country_code":"SK","type":"education","lineage":["https://openalex.org/I74788687"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"Martin \u0160koviera","raw_affiliation_strings":["Department of Computer Science Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovakia"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science Faculty of Mathematics, Physics and Informatics Comenius University 842 48 Bratislava, Slovakia","institution_ids":["https://openalex.org/I74788687"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038322764"],"corresponding_institution_ids":["https://openalex.org/I74788687"],"apc_list":null,"apc_paid":null,"fwci":1.1207,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.80662629,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"14","issue":"1","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":0.9987999796867371,"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"}},"topics":[{"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9955999851226807,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/vertex-connectivity","display_name":"Vertex connectivity","score":0.8427014350891113},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8198133707046509},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8146312236785889},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5154284238815308},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.44714128971099854},{"id":"https://openalex.org/keywords/cubic-graph","display_name":"Cubic graph","score":0.43187105655670166},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4292856752872467},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4159681499004364},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4037652015686035},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.14781856536865234},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.0751621425151825}],"concepts":[{"id":"https://openalex.org/C2983226441","wikidata":"https://www.wikidata.org/wiki/Q3115621","display_name":"Vertex connectivity","level":4,"score":0.8427014350891113},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8198133707046509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8146312236785889},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5154284238815308},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.44714128971099854},{"id":"https://openalex.org/C100500283","wikidata":"https://www.wikidata.org/wiki/Q1374495","display_name":"Cubic graph","level":5,"score":0.43187105655670166},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4292856752872467},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4159681499004364},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4037652015686035},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.14781856536865234},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.0751621425151825}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/936","is_oa":true,"landing_page_url":"https://doi.org/10.37236/936","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r18/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:CiteSeerX.psu:10.1.1.88.4","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.88.4","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.emis.de/journals/EJC/Volume_14/PDF/v14i1r18.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/936","is_oa":true,"landing_page_url":"https://doi.org/10.37236/936","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v14i1r18/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":[{"id":"https://openalex.org/F4320323641","display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","ror":"https://ror.org/044gwpv05"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3000716540.pdf","grobid_xml":"https://content.openalex.org/works/W3000716540.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W8184935","https://openalex.org/W757370673","https://openalex.org/W2006619685","https://openalex.org/W2022795828","https://openalex.org/W2023478138","https://openalex.org/W2035091205","https://openalex.org/W2087818742","https://openalex.org/W2093497699","https://openalex.org/W2326211873","https://openalex.org/W2477838342","https://openalex.org/W2613014342","https://openalex.org/W3032908210","https://openalex.org/W4234132957","https://openalex.org/W4241899069","https://openalex.org/W6606679931"],"related_works":["https://openalex.org/W2950817880","https://openalex.org/W3187181455","https://openalex.org/W2159586130","https://openalex.org/W2080725679","https://openalex.org/W2049969628","https://openalex.org/W2071797893","https://openalex.org/W1980648360","https://openalex.org/W3211032058","https://openalex.org/W4313216298","https://openalex.org/W2161951629"],"abstract_inverted_index":{"A":[0],"graph":[1],"is":[2,6],"hypohamiltonian":[3,19,23,41,66,89,94],"if":[4],"it":[5],"not":[7],"hamiltonian":[8],"but":[9,104],"every":[10],"vertex-deleted":[11],"subgraph":[12],"is.":[13],"In":[14],"this":[15],"paper":[16],"we":[17,50],"study":[18],"snarks":[20,42,67,78,95],"\u2013":[21],"cubic":[22],"graphs":[24,56],"with":[25,68,96],"chromatic":[26],"index":[27],"4.":[28],"We":[29],"describe":[30],"a":[31],"method,":[32],"based":[33],"on":[34],"superposition":[35],"of":[36,79,86],"snarks,":[37],"which":[38],"produces":[39,93],"new":[40],"from":[43],"old":[44],"ones.":[45],"By":[46],"choosing":[47],"suitable":[48],"ingredients":[49],"can":[51],"achieve":[52],"that":[53],"the":[54,76,82],"resulting":[55],"are":[57],"cyclically":[58,87],"$5$-connected":[59],"or":[60],"$6$-connected.":[61],"Previously,":[62],"only":[63,83],"three":[64],"sporadic":[65],"cyclic":[69,97],"connectivity":[70,98],"5":[71],"had":[72],"been":[73],"found,":[74],"while":[75],"flower":[77],"Isaacs":[80],"were":[81],"known":[84],"family":[85],"6-connected":[88],"snarks.":[90],"Our":[91],"method":[92],"$5$":[99],"and":[100],"$6$":[101],"for":[102],"all":[103],"finitely":[105],"many":[106],"even":[107],"orders.":[108]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
