{"id":"https://openalex.org/W2139828420","doi":"https://doi.org/10.1137/15m1047106","title":"Elegantly Colored Paths and Cycles in Edge Colored Random Graphs","display_name":"Elegantly Colored Paths and Cycles in Edge Colored Random Graphs","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2139828420","doi":"https://doi.org/10.1137/15m1047106","mag":"2139828420"},"language":"en","primary_location":{"id":"doi:10.1137/15m1047106","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1047106","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1403.1453","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031959875","display_name":"Lisa Espig","orcid":null},"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":"Lisa Espig","raw_affiliation_strings":["Carnegie Mellon University"],"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University","institution_ids":["https://openalex.org/I74973139"]}]},{"author_position":"middle","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":false,"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/A5008556299","display_name":"Michael Krivelevich","orcid":"https://orcid.org/0000-0003-2357-4982"},"institutions":[{"id":"https://openalex.org/I16391192","display_name":"Tel Aviv University","ror":"https://ror.org/04mhzgx49","country_code":"IL","type":"education","lineage":["https://openalex.org/I16391192"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Michael Krivelevich","raw_affiliation_strings":["Tel-Aviv  University"],"affiliations":[{"raw_affiliation_string":"Tel-Aviv  University","institution_ids":["https://openalex.org/I16391192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031959875"],"corresponding_institution_ids":["https://openalex.org/I74973139"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.01124297,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"32","issue":"3","first_page":"1585","last_page":"1618"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T11476","display_name":"Graph theory and applications","score":0.9976999759674072,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9976000189781189,"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":0.787114143371582},{"id":"https://openalex.org/keywords/colored","display_name":"Colored","score":0.7858433723449707},{"id":"https://openalex.org/keywords/hamiltonian-path","display_name":"Hamiltonian path","score":0.6090880632400513},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6065903902053833},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5977416038513184},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.5686801671981812},{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.5368211269378662},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42899924516677856},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3780513405799866},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21183988451957703}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.787114143371582},{"id":"https://openalex.org/C2778307483","wikidata":"https://www.wikidata.org/wiki/Q5149038","display_name":"Colored","level":2,"score":0.7858433723449707},{"id":"https://openalex.org/C86524685","wikidata":"https://www.wikidata.org/wiki/Q273037","display_name":"Hamiltonian path","level":3,"score":0.6090880632400513},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6065903902053833},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5977416038513184},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.5686801671981812},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.5368211269378662},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42899924516677856},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3780513405799866},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21183988451957703},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials 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":13,"locations":[{"id":"doi:10.1137/15m1047106","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1047106","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1403.1453","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1403.1453","pdf_url":"https://arxiv.org/pdf/1403.1453","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:2139828420","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1403.1453.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:repository.cmu.edu:math-1746","is_oa":false,"landing_page_url":"http://repository.cmu.edu/cgi/viewcontent.cgi?article=1746&context=math","pdf_url":null,"source":{"id":"https://openalex.org/S4306400668","display_name":"Research Showcase @ Carnegie Mellon University (Carnegie Mellon University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I74973139","host_organization_name":"Carnegie Mellon University","host_organization_lineage":["https://openalex.org/I74973139"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of Mathematical Sciences","raw_type":"text"},{"id":"pmh:doi:10.1184/r1/6477308","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal contribution"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.434.4255","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.434.4255","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.tau.ac.il/~krivelev/zebraic.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.638.8653","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.638.8653","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/~af1p/Texfiles/zebraic.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.721.2698","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.721.2698","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.cmu.edu/%7Eaf1p/Texfiles/zebraic.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.757.7777","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.757.7777","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1403.1453.pdf","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/6477308","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Elegantly_colored_paths_and_cycles_in_edge_colored_random_graphs/6477308","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"doi:10.48550/arxiv.1403.1453","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1403.1453","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.1184/r1/6477308","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6477308","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.1184/r1/6477308.v1","is_oa":true,"landing_page_url":"https://doi.org/10.1184/r1/6477308.v1","pdf_url":null,"source":{"id":"https://openalex.org/S7407050927","display_name":"KiltHub Repository","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1403.1453","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1403.1453","pdf_url":"https://arxiv.org/pdf/1403.1453","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3306346009","display_name":null,"funder_award_id":"DMS-6721878","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"},{"id":"https://openalex.org/F4320320950","display_name":"United States-Israel Binational Science Foundation","ror":"https://ror.org/00j8z2m73"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W108214179","https://openalex.org/W1759514461","https://openalex.org/W1824248119","https://openalex.org/W1937563492","https://openalex.org/W1980608991","https://openalex.org/W1983077071","https://openalex.org/W2007501353","https://openalex.org/W2007550461","https://openalex.org/W2062587363","https://openalex.org/W2083870048","https://openalex.org/W2111559003","https://openalex.org/W2118882118","https://openalex.org/W2241838543","https://openalex.org/W2279529641","https://openalex.org/W2336317531","https://openalex.org/W2950022103","https://openalex.org/W2963989835","https://openalex.org/W3121789757","https://openalex.org/W3144881883"],"related_works":["https://openalex.org/W2042185700","https://openalex.org/W2158796492","https://openalex.org/W3104596862","https://openalex.org/W1487824761","https://openalex.org/W2966511226","https://openalex.org/W2741646780","https://openalex.org/W299706678","https://openalex.org/W2127936896","https://openalex.org/W2305135413","https://openalex.org/W2135737379","https://openalex.org/W2402141030","https://openalex.org/W2140790988","https://openalex.org/W2950140953","https://openalex.org/W2950197217","https://openalex.org/W2029596791","https://openalex.org/W2068970707","https://openalex.org/W1947677090","https://openalex.org/W2950774858","https://openalex.org/W2131538679","https://openalex.org/W2952190991"],"abstract_inverted_index":{"We":[0,6,33,68,77,102,126,140],"first":[1,53],"consider":[2,128,143],"the":[3,40,47,52,61,65,74,96,100,106],"following":[4,75],"problem.":[5,76],"are":[7,56],"given":[8],"a":[9,23,28,110],"fixed":[10],"perfect":[11],"matching":[12],"$M$":[13],"of":[14,123],"$[n]$":[15],"and":[16,81,132],"we":[17],"add":[18],"random":[19,66,79],"edges":[20,80],"one":[21,121],"at":[22,119],"time":[24,42,54,108],"until":[25],"there":[26,55],"is":[27,46,90],"Hamilton":[29,112],"cycle":[30,113],"containing":[31],"$M$.":[32],"show":[34,103],"that":[35,50,104],"with":[36,115],"high":[37],"probability":[38],"(w.h.p.)":[39],"hitting":[41,107],"for":[43,51,73,109],"this":[44,71],"event":[45],"same":[48],"as":[49],"no":[57],"isolated":[58],"vertices":[59],"in":[60],"graph":[62],"induced":[63],"by":[64],"edges.":[67],"then":[69,127],"use":[70],"result":[72],"generate":[78],"randomly":[82],"color":[83],"them":[84],"black":[85],"or":[86],"white.":[87],"A":[88],"path/cycle":[89],"said":[91],"to":[92,137],"be":[93],"zebraic":[94,111],"if":[95],"colors":[97],"alternate":[98],"along":[99],"path.":[101],"w.h.p.":[105],"coincides":[114],"every":[116],"vertex":[117],"meeting":[118],"least":[120],"edge":[122],"each":[124],"color.":[125],"some":[129],"related":[130],"problems":[131],"(partially)":[133],"extend":[134],"our":[135],"results":[136],"multiple":[138],"colors.":[139],"also":[141],"briefly":[142],"directed":[144],"versions.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}