{"id":"https://openalex.org/W2122123300","doi":"https://doi.org/10.1017/s0963548305006760","title":"On Cover Graphs and Dependent Arcs in Acyclic Orientations","display_name":"On Cover Graphs and Dependent Arcs in Acyclic Orientations","publication_year":2005,"publication_date":"2005-07-01","ids":{"openalex":"https://openalex.org/W2122123300","doi":"https://doi.org/10.1017/s0963548305006760","mag":"2122123300"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548305006760","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548305006760","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://digitalcommons.uri.edu/math_facpubs/248","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109115706","display_name":"V. R\u00f6dl","orcid":null},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"V. R\u00d6DL","raw_affiliation_strings":["Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30032, USA (e-mail:","Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30032, USA (e-mail: rodl@mathcs.emory.edu)#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30032, USA (e-mail:","institution_ids":["https://openalex.org/I150468666"]},{"raw_affiliation_string":"Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30032, USA (e-mail: rodl@mathcs.emory.edu)#TAB#","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112445207","display_name":"Lubo\u0161 Thoma","orcid":null},"institutions":[{"id":"https://openalex.org/I17626003","display_name":"University of Rhode Island","ror":"https://ror.org/013ckk937","country_code":"US","type":"education","lineage":["https://openalex.org/I17626003"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"L. THOMA","raw_affiliation_strings":["Department of Mathematics, University of Rhode Island, Kingston RI 02881, USA (e-mail:","Department of Mathematics, University of Rhode Island, Kingston RI 02881, USA (e-mail: thoma@math.uri.edu)#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Rhode Island, Kingston RI 02881, USA (e-mail:","institution_ids":["https://openalex.org/I17626003"]},{"raw_affiliation_string":"Department of Mathematics, University of Rhode Island, Kingston RI 02881, USA (e-mail: thoma@math.uri.edu)#TAB#","institution_ids":["https://openalex.org/I17626003"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5109115706"],"corresponding_institution_ids":["https://openalex.org/I150468666"],"apc_list":null,"apc_paid":null,"fwci":0.4491,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.61917684,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"14","issue":"4","first_page":"585","last_page":"617"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9994999766349792,"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":0.9979000091552734,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9947999715805054,"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/combinatorics","display_name":"Combinatorics","score":0.7270946502685547},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.6673750877380371},{"id":"https://openalex.org/keywords/directed-acyclic-graph","display_name":"Directed acyclic graph","score":0.618515133857727},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5087078213691711},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.433937668800354},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3868297338485718},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.0854220986366272}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7270946502685547},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.6673750877380371},{"id":"https://openalex.org/C74197172","wikidata":"https://www.wikidata.org/wiki/Q1195339","display_name":"Directed acyclic graph","level":2,"score":0.618515133857727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5087078213691711},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.433937668800354},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3868297338485718},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0854220986366272},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548305006760","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548305006760","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.uri.edu:math_facpubs-1250","is_oa":true,"landing_page_url":"https://digitalcommons.uri.edu/math_facpubs/248","pdf_url":null,"source":{"id":"https://openalex.org/S2764761010","display_name":"Journal of Media Literacy Education","issn_l":"2167-8715","issn":["2167-8715"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310316378","host_organization_name":"National Association for Media Literacy Education","host_organization_lineage":["https://openalex.org/P4310316378"],"host_organization_lineage_names":["National Association for Media Literacy Education"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Faculty Publications","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:digitalcommons.uri.edu:math_facpubs-1250","is_oa":true,"landing_page_url":"https://digitalcommons.uri.edu/math_facpubs/248","pdf_url":null,"source":{"id":"https://openalex.org/S2764761010","display_name":"Journal of Media Literacy Education","issn_l":"2167-8715","issn":["2167-8715"],"is_oa":false,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310316378","host_organization_name":"National Association for Media Literacy Education","host_organization_lineage":["https://openalex.org/P4310316378"],"host_organization_lineage_names":["National Association for Media Literacy Education"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics Faculty Publications","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1969653383","https://openalex.org/W1997059040","https://openalex.org/W2014400460","https://openalex.org/W2029810714","https://openalex.org/W2047452808","https://openalex.org/W2054018639","https://openalex.org/W2068871408","https://openalex.org/W2153478982","https://openalex.org/W2523605171","https://openalex.org/W2905110430"],"related_works":["https://openalex.org/W2731094954","https://openalex.org/W2789273959","https://openalex.org/W4302345037","https://openalex.org/W2952978498","https://openalex.org/W2951616510","https://openalex.org/W3122467582","https://openalex.org/W1763561501","https://openalex.org/W4292730466","https://openalex.org/W623607250","https://openalex.org/W4297794376"],"abstract_inverted_index":{"The":[0,17],"present":[1],"paper":[2],"deals":[3],"with":[4,168],"two":[5],"graph":[6,22,121],"parameters":[7],"related":[8],"to":[9,48,54],"cover":[10,57],"graphs":[11,166],"and":[12,31,103,172,199],"acyclic":[13,117,147],"orientations":[14],"of":[15,20,44,119,142,149,160,165,191],"graphs.":[16],"parameter":[18],"$c(G)$":[19],"a":[21,56,120],"$G$":[23,51,122,150,167],",":[24,68,123,159],"introduced":[25],"by":[26,157],"B.":[27,201],"Bollob\u00e1s,":[28],"G.":[29],"Brightwell":[30],"J.":[32,204],"Ne\u0161et\u0159il":[33],"[":[34,203],"Order":[35],"3":[36],"245\u2013255],":[37],"is":[38,111,126],"defined":[39],"as":[40,82,84,107],"the":[41,112,139,154,163],"minimum":[42,140],"number":[43,141,170],"edges":[45],"one":[46],"needs":[47],"delete":[49],"from":[50],"in":[52,145,162],"order":[53],"obtain":[55],"graph.":[58,114],"Extending":[59],"their":[60],"results,":[61],"we":[62,177],"prove":[63],"that,":[64],"for":[65,98],"$\\delta":[66],"&gt;0$":[67],"$(1-\\delta)":[69],"\\frac{1}{l}":[70,77],"\\frac{n^2p}{2}":[71],"\\leq":[72,75,89,91],"c({\\mathcal":[73],"G}_{n,p})":[74],"(1+\\delta)":[76],"\\frac{n^2p}{2}$":[78],"asymptotically":[79],"almost":[80],"surely":[81],"long":[83],"$C":[85],"n^{-1":[86,93],"+":[87,94],"\\frac{1}{l}}":[88],"p(n)":[90],"c":[92],"\\frac{1}{":[95],"l-1}":[96],"}$":[97],"some":[99],"positive":[100],"constants":[101],"$c$":[102],"$C$":[104],".":[105,151,175,187],"Here,":[106],"usual,":[108],"${\\mathcal":[109],"G}_{n,p}$":[110],"random":[113],"Given":[115],"an":[116,124,133],"orientation":[118,148],"arc":[125],"called":[127],"dependent":[128,143],"if":[129],"its":[130],"reversal":[131],"creates":[132],"oriented":[134],"cycle.":[135],"Let":[136],"$d_{\\min}(G)$":[137],"be":[138],"arcs":[144],"any":[146],"We":[152],"determine":[153],"supremum,":[155],"denoted":[156],"$r_{\\chi,g}$":[158],"$d_{\\min}(G)/e(G)$":[161],"class":[164],"chromatic":[169],"$\\chi$":[171],"girth":[173],"$g$":[174],"Namely,":[176],"show":[178],"that":[179],"$r_{\\chi,g}":[180],"=":[181],"{(\\scriptsize\\begin{array}{@{}c@{}}{\\chi}-g+2\\\\":[182],"2\\end{array})}":[183],"/":[184],"{(\\scriptsize\\begin{array}{@{}c@{}}{\\chi}\\\\":[185],"2\\end{array})}$":[186],"This":[188],"extends":[189],"results":[190],"D.":[192,200],"C.":[193],"Fisher,":[194],"K.":[195],"Fraughnaugh,":[196],"L.":[197],"Langley":[198],"West":[202],"Combin.":[205],"Theory":[206],"Ser.":[207],"B":[208],"71":[209],"73\u201378].":[210]},"counts_by_year":[{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
