{"id":"https://openalex.org/W2153123938","doi":"https://doi.org/10.37236/4673","title":"Between 2- and 3-Colorability","display_name":"Between 2- and 3-Colorability","publication_year":2015,"publication_date":"2015-02-16","ids":{"openalex":"https://openalex.org/W2153123938","doi":"https://doi.org/10.37236/4673","mag":"2153123938"},"language":"en","primary_location":{"id":"doi:10.37236/4673","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4673","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p34/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v22i1p34/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056950019","display_name":"Alan Frieze","orcid":"https://orcid.org/0000-0002-8481-5615"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Alan Frieze","raw_affiliation_strings":["Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054318475","display_name":"Wesley Pegden","orcid":"https://orcid.org/0000-0002-3680-1817"},"institutions":[{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wesley Pegden","raw_affiliation_strings":["Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056950019"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":1.3632,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.78300921,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"1","first_page":null,"last_page":null},"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":0.9973999857902527,"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":0.9973999857902527,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9573000073432922,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9373000264167786,"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":0.8789240121841431},{"id":"https://openalex.org/keywords/homomorphism","display_name":"Homomorphism","score":0.878243088722229},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8682376742362976},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.617874264717102},{"id":"https://openalex.org/keywords/girth","display_name":"Girth (graph theory)","score":0.43091216683387756},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.329363077878952}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8789240121841431},{"id":"https://openalex.org/C4042151","wikidata":"https://www.wikidata.org/wiki/Q215111","display_name":"Homomorphism","level":2,"score":0.878243088722229},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8682376742362976},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.617874264717102},{"id":"https://openalex.org/C2777434295","wikidata":"https://www.wikidata.org/wiki/Q959831","display_name":"Girth (graph theory)","level":2,"score":0.43091216683387756},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.329363077878952},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/4673","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4673","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p34/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:10.37236/4673","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4673","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i1p34/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G4797868072","display_name":"New directions arising from a special diffusion process on the integer lattice","funder_award_id":"1363136","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6717149835","display_name":"AF:  Small:  Probabilistic Considerations in the Analysis of Algorithms","funder_award_id":"1013110","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2153123938.pdf","grobid_xml":"https://content.openalex.org/works/W2153123938.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1526979981","https://openalex.org/W1559492868","https://openalex.org/W1978113428","https://openalex.org/W1988522098","https://openalex.org/W2005394933","https://openalex.org/W2017458202","https://openalex.org/W2060664509","https://openalex.org/W2065484772","https://openalex.org/W2164437357","https://openalex.org/W2905110430","https://openalex.org/W3144881883","https://openalex.org/W4243627882","https://openalex.org/W4247023489"],"related_works":["https://openalex.org/W4308159138","https://openalex.org/W1979798674","https://openalex.org/W3169947911","https://openalex.org/W4327811209","https://openalex.org/W3037616202","https://openalex.org/W390508480","https://openalex.org/W2375240985","https://openalex.org/W2963079901","https://openalex.org/W2171111248","https://openalex.org/W3036423744"],"abstract_inverted_index":{"We":[0,18],"consider":[1],"the":[2,5,53,93],"question":[3],"of":[4,7,76,95],"existence":[6,94],"homomorphisms":[8],"between":[9],"$G_{n,p}$":[10,35,40,68,87],"and":[11,109],"odd":[12],"cycles":[13],"when":[14],"$p=c/n$,":[15],"$1<c\\leq":[16],"4$.":[17],"show":[19,57],"that":[20,30,58,72,81,111],"for":[21,105],"any":[22],"positive":[23],"integer":[24],"$\\ell$,":[25],"there":[26,63,82],"exists":[27],"$\\epsilon=\\epsilon(\\ell)$":[28],"such":[29],"if":[31,59],"$c=1+\\epsilon$":[32],"then":[33,61],"w.h.p.":[34,62,116],"has":[36],"a":[37,84],"homomorphism":[38,66,85],"from":[39,67,86],"to":[41,69,88],"$C_{2\\ell+1}$":[42],"so":[43],"long":[44],"as":[45],"its":[46],"odd-girth":[47],"is":[48,64,83],"at":[49],"least":[50],"$2\\ell+1$.":[51],"On":[52],"other":[54],"hand,":[55],"we":[56],"$c=4$":[60],"no":[65],"$C_5$.":[70],"Note":[71],"in":[73],"our":[74],"range":[75],"interest,":[77],"$\\chi(G_{n,p})=3$":[78],"w.h.p.,":[79],"implying":[80],"$C_3$.":[89],"These":[90],"results":[91],"imply":[92],"random":[96],"graphs":[97],"with":[98],"circular":[99],"chromatic":[100],"numbers":[101],"$\\chi_c$":[102],"satisfying":[103],"$2<\\chi_c(G)<2+\\delta$":[104],"arbitrarily":[106],"small":[107],"$\\delta$,":[108],"also":[110],"$2.5\\leq":[112],"\\chi_c(G_{n,\\frac":[113],"4":[114],"n})<3$":[115]},"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-03-15T09:29:46.208133","created_date":"2025-10-10T00:00:00"}