{"id":"https://openalex.org/W1564731995","doi":"https://doi.org/10.37236/2388","title":"Asymptotic Lower Bounds on Circular Chromatic Index of Snarks","display_name":"Asymptotic Lower Bounds on Circular Chromatic Index of Snarks","publication_year":2013,"publication_date":"2013-04-09","ids":{"openalex":"https://openalex.org/W1564731995","doi":"https://doi.org/10.37236/2388","mag":"1564731995"},"language":"en","primary_location":{"id":"doi:10.37236/2388","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2388","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p2/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/v20i2p2/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083500938","display_name":"Martin M\u00e1\u010daj","orcid":null},"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 Ma\u010daj","raw_affiliation_strings":["Comenius University, Bratislava","Comenius University, Bratislava;"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Comenius University, Bratislava","institution_ids":["https://openalex.org/I74788687"]},{"raw_affiliation_string":"Comenius University, Bratislava;","institution_ids":["https://openalex.org/I74788687"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050025544","display_name":"J\u00e1n Maz\u00e1k","orcid":"https://orcid.org/0000-0002-6498-9984"},"institutions":[{"id":"https://openalex.org/I144246526","display_name":"University of Trnava","ror":"https://ror.org/05nj8rv48","country_code":"SK","type":"education","lineage":["https://openalex.org/I144246526"]}],"countries":["SK"],"is_corresponding":false,"raw_author_name":"J\u00e1n Maz\u00e1k","raw_affiliation_strings":["Trnava University, Trnava"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Trnava University, Trnava","institution_ids":["https://openalex.org/I144246526"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04067862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"2","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":0.9994999766349792,"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":0.9994999766349792,"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/T11476","display_name":"Graph theory and applications","score":0.9973999857902527,"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/T12149","display_name":"Nanocluster Synthesis and Applications","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8859472274780273},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8207536935806274},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.7010181546211243},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6358731985092163},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.6040730476379395},{"id":"https://openalex.org/keywords/chromatic-scale","display_name":"Chromatic scale","score":0.5818519592285156},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5402945876121521},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5274180173873901},{"id":"https://openalex.org/keywords/foster-graph","display_name":"Foster graph","score":0.4248707890510559},{"id":"https://openalex.org/keywords/index","display_name":"Index (typography)","score":0.4129011631011963},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3850194215774536},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15026819705963135},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.06580838561058044}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8859472274780273},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8207536935806274},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.7010181546211243},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6358731985092163},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.6040730476379395},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.5818519592285156},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5402945876121521},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5274180173873901},{"id":"https://openalex.org/C68996132","wikidata":"https://www.wikidata.org/wiki/Q3115485","display_name":"Foster graph","level":5,"score":0.4248707890510559},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.4129011631011963},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3850194215774536},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15026819705963135},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.06580838561058044},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/2388","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2388","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p2/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"}],"best_oa_location":{"id":"doi:10.37236/2388","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2388","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i2p2/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":[{"id":"https://openalex.org/G223322507","display_name":null,"funder_award_id":"-0223-10","funder_id":"https://openalex.org/F4320323251","funder_display_name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja"},{"id":"https://openalex.org/G3389480260","display_name":null,"funder_award_id":"ESF-EC-0009-10","funder_id":"https://openalex.org/F4320320301","funder_display_name":"European Science Foundation"},{"id":"https://openalex.org/G4358634787","display_name":"Geometrick\u00e9 reprezent\u00e1cie a symetrie grafov, m\u00e1p a in\u00fdch diskr\u00e9tnych \u0161trukt\u00far s aplik\u00e1ciami vo vede","funder_award_id":"ESF-EC-0009-10","funder_id":"https://openalex.org/F4320323251","funder_display_name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja"},{"id":"https://openalex.org/G7746802177","display_name":null,"funder_award_id":"0111-07","funder_id":"https://openalex.org/F4320323251","funder_display_name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja"}],"funders":[{"id":"https://openalex.org/F4320320301","display_name":"European Science Foundation","ror":"https://ror.org/04esata81"},{"id":"https://openalex.org/F4320323251","display_name":"Agent\u00fara na Podporu V\u00fdskumu a V\u00fdvoja","ror":"https://ror.org/037nx0e70"},{"id":"https://openalex.org/F4320323641","display_name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","ror":"https://ror.org/044gwpv05"},{"id":"https://openalex.org/F4320338080","display_name":"European Social Fund","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1564731995.pdf","grobid_xml":"https://content.openalex.org/works/W1564731995.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W36880984","https://openalex.org/W1577585318","https://openalex.org/W1613557267","https://openalex.org/W1994701365","https://openalex.org/W1995620335","https://openalex.org/W2013273488","https://openalex.org/W2032134740","https://openalex.org/W2035091205","https://openalex.org/W2056289686","https://openalex.org/W2081236892","https://openalex.org/W2097200419","https://openalex.org/W2116902851","https://openalex.org/W2130738665","https://openalex.org/W2951550992","https://openalex.org/W2999040677","https://openalex.org/W4231329390","https://openalex.org/W4241899069","https://openalex.org/W4246110625","https://openalex.org/W4251997028","https://openalex.org/W6600042225"],"related_works":["https://openalex.org/W2371809914","https://openalex.org/W2019936340","https://openalex.org/W2237219011","https://openalex.org/W4210604868","https://openalex.org/W1993409199","https://openalex.org/W2049992750","https://openalex.org/W2091414672","https://openalex.org/W2964184200","https://openalex.org/W2797469516","https://openalex.org/W4302768836"],"abstract_inverted_index":{"We":[0,37],"prove":[1],"that":[2,40,82],"the":[3,41,45,83,88],"circular":[4,69,84],"chromatic":[5,16,70,85],"index":[6,17,71,86],"of":[7,32,87],"a":[8],"cubic":[9,33],"graph":[10],"$G$":[11,62],"with":[12,53],"$2k$":[13],"vertices":[14],"and":[15],"$4$":[18],"is":[19,25,72,95],"at":[20,65,73],"least":[21,66,74],"$3+2/k$.":[22],"This":[23],"bound":[24,47],"(asymptotically)":[26],"optimal":[27],"for":[28,51],"an":[29,79],"infinite":[30],"class":[31],"graphs":[34,52],"containing":[35],"bridges.":[36],"also":[38],"show":[39],"constant":[42],"$2$":[43],"in":[44],"above":[46],"can":[48],"be":[49],"increased":[50],"larger":[54],"girth":[55,64],"or":[56],"higher":[57],"connectivity.":[58],"In":[59],"particular,":[60],"if":[61],"has":[63],"$5$,":[67],"its":[68],"$3+2.5/k$.":[75],"Our":[76],"method":[77],"gives":[78],"alternative":[80],"proof":[81],"generalised":[89],"type":[90],"1":[91],"Blanu\u0161a":[92],"snark":[93],"$B_m^1$":[94],"$3+2/3m$.":[96]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}