{"id":"https://openalex.org/W2146303279","doi":"https://doi.org/10.37236/2498","title":"An Iterative Approach to the Traceability Conjecture for Oriented Graphs","display_name":"An Iterative Approach to the Traceability Conjecture for Oriented Graphs","publication_year":2013,"publication_date":"2013-03-24","ids":{"openalex":"https://openalex.org/W2146303279","doi":"https://doi.org/10.37236/2498","mag":"2146303279"},"language":"en","primary_location":{"id":"doi:10.37236/2498","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2498","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p59/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/v20i1p59/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014639430","display_name":"Susan Van Aardt","orcid":null},"institutions":[{"id":"https://openalex.org/I165390105","display_name":"University of South Africa","ror":"https://ror.org/048cwvf49","country_code":"ZA","type":"education","lineage":["https://openalex.org/I165390105"]}],"countries":["ZA"],"is_corresponding":true,"raw_author_name":"Susan Van Aardt","raw_affiliation_strings":["University of South Africa"],"affiliations":[{"raw_affiliation_string":"University of South Africa","institution_ids":["https://openalex.org/I165390105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110460350","display_name":"Alewyn P. Burger","orcid":null},"institutions":[{"id":"https://openalex.org/I26092322","display_name":"Stellenbosch University","ror":"https://ror.org/05bk57929","country_code":"ZA","type":"education","lineage":["https://openalex.org/I26092322"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Alewyn Burger","raw_affiliation_strings":["University of Stellenbosch"],"affiliations":[{"raw_affiliation_string":"University of Stellenbosch","institution_ids":["https://openalex.org/I26092322"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108652044","display_name":"Jean E. Dunbar","orcid":null},"institutions":[{"id":"https://openalex.org/I206204273","display_name":"Converse College","ror":"https://ror.org/01g0q1j14","country_code":"US","type":"education","lineage":["https://openalex.org/I206204273"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jean Dunbar","raw_affiliation_strings":["Converse College","Converse College ,"],"affiliations":[{"raw_affiliation_string":"Converse College","institution_ids":["https://openalex.org/I206204273"]},{"raw_affiliation_string":"Converse College ,","institution_ids":["https://openalex.org/I206204273"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056680244","display_name":"Marietjie Frick","orcid":"https://orcid.org/0000-0002-5011-604X"},"institutions":[{"id":"https://openalex.org/I165390105","display_name":"University of South Africa","ror":"https://ror.org/048cwvf49","country_code":"ZA","type":"education","lineage":["https://openalex.org/I165390105"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Marietjie Frick","raw_affiliation_strings":["University of South Africa"],"affiliations":[{"raw_affiliation_string":"University of South Africa","institution_ids":["https://openalex.org/I165390105"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019069616","display_name":"John M. Harris","orcid":null},"institutions":[{"id":"https://openalex.org/I86115722","display_name":"Furman University","ror":"https://ror.org/04ytb9n23","country_code":"US","type":"education","lineage":["https://openalex.org/I86115722"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Harris","raw_affiliation_strings":["Furman University"],"affiliations":[{"raw_affiliation_string":"Furman University","institution_ids":["https://openalex.org/I86115722"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048266029","display_name":"Joy Singleton","orcid":null},"institutions":[{"id":"https://openalex.org/I165390105","display_name":"University of South Africa","ror":"https://ror.org/048cwvf49","country_code":"ZA","type":"education","lineage":["https://openalex.org/I165390105"]}],"countries":["ZA"],"is_corresponding":false,"raw_author_name":"Joy Singleton","raw_affiliation_strings":["University of South Africa"],"affiliations":[{"raw_affiliation_string":"University of South Africa","institution_ids":["https://openalex.org/I165390105"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5014639430"],"corresponding_institution_ids":["https://openalex.org/I165390105"],"apc_list":null,"apc_paid":null,"fwci":1.8493,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.86402607,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"20","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":0.9994999766349792,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9894000291824341,"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":0.9864000082015991,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/traceability","display_name":"Traceability","score":0.7717618942260742},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.7589901089668274},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.692797064781189},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6617704629898071},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6598654985427856},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6089799404144287},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5231327414512634},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.41697701811790466},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.042919158935546875}],"concepts":[{"id":"https://openalex.org/C153876917","wikidata":"https://www.wikidata.org/wiki/Q899704","display_name":"Traceability","level":2,"score":0.7717618942260742},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.7589901089668274},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.692797064781189},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6617704629898071},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6598654985427856},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6089799404144287},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5231327414512634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41697701811790466},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.042919158935546875},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/2498","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2498","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p59/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:10.37236/2498","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2498","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v20i1p59/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/G3034753964","display_name":null,"funder_award_id":"grant","funder_id":"https://openalex.org/F4320320671","funder_display_name":"National Research Foundation"}],"funders":[{"id":"https://openalex.org/F4320320671","display_name":"National Research Foundation","ror":"https://ror.org/05s0g1g46"},{"id":"https://openalex.org/F4320324956","display_name":"University of South Africa","ror":"https://ror.org/048cwvf49"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2146303279.pdf","grobid_xml":"https://content.openalex.org/works/W2146303279.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1548164611","https://openalex.org/W1990731595","https://openalex.org/W2006016709","https://openalex.org/W2015549411","https://openalex.org/W2016857938","https://openalex.org/W2031908930","https://openalex.org/W2046267970","https://openalex.org/W2062928364","https://openalex.org/W2090123683","https://openalex.org/W2113147502"],"related_works":["https://openalex.org/W2038088825","https://openalex.org/W1975203667","https://openalex.org/W2370328482","https://openalex.org/W4287882779","https://openalex.org/W2046896701","https://openalex.org/W2378709054","https://openalex.org/W2265849288","https://openalex.org/W2140169421","https://openalex.org/W4380301954","https://openalex.org/W1996632063"],"abstract_inverted_index":{"A":[0],"digraph":[1],"is":[2,7,19,39,54,82,93],"$k$-traceable":[3,31,51],"if":[4],"its":[5,14],"order":[6,17,35,78,89],"at":[8,36,79,90],"least":[9,37,80,91],"$k$":[10,18],"and":[11,84],"each":[12],"of":[13,16,34,77,88],"subdigraphs":[15],"traceable.":[20,40,55,94],"The":[21],"Traceability":[22],"Conjecture":[23],"(TC)":[24],"states":[25],"that":[26,45,72],"for":[27,46],"$k\\geq":[28],"2$":[29],"every":[30,50,73,85],"oriented":[32,52,75],"graph":[33,53,76,87],"$2k-1$":[38],"It":[41],"has":[42],"been":[43],"shown":[44],"$2\\leq":[47],"k\\leq":[48],"6$,":[49],"We":[56],"develop":[57],"an":[58],"iterative":[59],"procedure":[60],"to":[61],"extend":[62],"previous":[63],"results":[64],"regarding":[65],"the":[66],"TC.":[67],"In":[68],"particular,":[69],"we":[70],"prove":[71],"$7$-traceable":[74],"9":[81],"traceable":[83],"8-traceable":[86],"14":[92]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
