{"id":"https://openalex.org/W1591666335","doi":"https://doi.org/10.37236/405","title":"Coloring the Edges of a Random Graph without a Monochromatic Giant Component","display_name":"Coloring the Edges of a Random Graph without a Monochromatic Giant Component","publication_year":2010,"publication_date":"2010-10-05","ids":{"openalex":"https://openalex.org/W1591666335","doi":"https://doi.org/10.37236/405","mag":"1591666335"},"language":"en","primary_location":{"id":"doi:10.37236/405","is_oa":true,"landing_page_url":"https://doi.org/10.37236/405","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r133/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/v17i1r133/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041974050","display_name":"Reto Sp\u00f6hel","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Reto Sp\u00f6hel","raw_affiliation_strings":["Institute of Theoretical Computer Science ETH Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institute of Theoretical Computer Science ETH Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062687538","display_name":"Angelika Steger","orcid":"https://orcid.org/0000-0002-3465-3996"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Angelika Steger","raw_affiliation_strings":["Institute of Theoretical Computer Science ETH Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institute of Theoretical Computer Science ETH Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070015080","display_name":"Henning Thomas","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Henning Thomas","raw_affiliation_strings":["Institute of Theoretical Computer Science ETH Z\u00fcrich, Switzerland"],"affiliations":[{"raw_affiliation_string":"Institute of Theoretical Computer Science ETH Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041974050"],"corresponding_institution_ids":["https://openalex.org/I35440088"],"apc_list":null,"apc_paid":null,"fwci":0.3726,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.54716497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9688000082969666,"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"}},"topics":[{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9688000082969666,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9656999707221985,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9135000109672546,"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":0.8630598783493042},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8439354300498962},{"id":"https://openalex.org/keywords/random-graph","display_name":"Random graph","score":0.6180704236030579},{"id":"https://openalex.org/keywords/monochromatic-color","display_name":"Monochromatic color","score":0.5704988837242126},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5148031115531921},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45629337430000305},{"id":"https://openalex.org/keywords/giant-component","display_name":"Giant component","score":0.44027864933013916},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4363091289997101},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.42578384280204773},{"id":"https://openalex.org/keywords/random-regular-graph","display_name":"Random regular graph","score":0.41939622163772583},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.4136281907558441},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.2675884962081909},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.194595068693161},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.15011712908744812},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06648683547973633}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8630598783493042},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8439354300498962},{"id":"https://openalex.org/C47458327","wikidata":"https://www.wikidata.org/wiki/Q910404","display_name":"Random graph","level":3,"score":0.6180704236030579},{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.5704988837242126},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5148031115531921},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45629337430000305},{"id":"https://openalex.org/C148818006","wikidata":"https://www.wikidata.org/wiki/Q4137985","display_name":"Giant component","level":4,"score":0.44027864933013916},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4363091289997101},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.42578384280204773},{"id":"https://openalex.org/C4255713","wikidata":"https://www.wikidata.org/wiki/Q7291988","display_name":"Random regular graph","level":5,"score":0.41939622163772583},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.4136281907558441},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.2675884962081909},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.194595068693161},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.15011712908744812},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06648683547973633},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/405","is_oa":true,"landing_page_url":"https://doi.org/10.37236/405","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r133/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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.187.8489","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.187.8489","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_17/PDF/v17i1r133.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/405","is_oa":true,"landing_page_url":"https://doi.org/10.37236/405","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r133/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/G1441312571","display_name":null,"funder_award_id":"00020","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G3423950586","display_name":null,"funder_award_id":"200021-120284","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G451236005","display_name":null,"funder_award_id":"200020-119918","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G4836148144","display_name":null,"funder_award_id":"20002","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5178539184","display_name":"The KLR-conjecture and Szemeredi's regularity in the sparse setting","funder_award_id":"119918","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5254711117","display_name":"Dynamism in Networks and Distributed Computations","funder_award_id":"120284","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5256785375","display_name":null,"funder_award_id":"200021-","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5599649393","display_name":null,"funder_award_id":"200020","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G628552264","display_name":null,"funder_award_id":"200020","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G766801546","display_name":"Das Sch\u00f6ne als Thema evangelischer Theologie, Friedrich-Wilhelms-Universit\u00e4t Bonn, Abteilung f\u00fcr praktische Theologie, Bonn/D","funder_award_id":"20284","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G993971353","display_name":null,"funder_award_id":"200021","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1591666335.pdf","grobid_xml":"https://content.openalex.org/works/W1591666335.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W365256087","https://openalex.org/W1515742382","https://openalex.org/W1591666335","https://openalex.org/W2004427634","https://openalex.org/W2033468284","https://openalex.org/W2052719937","https://openalex.org/W2065663455","https://openalex.org/W2095403663","https://openalex.org/W2152026596","https://openalex.org/W3142570770","https://openalex.org/W4231943475","https://openalex.org/W4244198819","https://openalex.org/W6630977895","https://openalex.org/W6649452411","https://openalex.org/W6666967911","https://openalex.org/W6721489647"],"related_works":["https://openalex.org/W2950850272","https://openalex.org/W2182339161","https://openalex.org/W4248914732","https://openalex.org/W4387641633","https://openalex.org/W2497425261","https://openalex.org/W2290279467","https://openalex.org/W1672624114","https://openalex.org/W2130919150","https://openalex.org/W4381245757","https://openalex.org/W2061292276"],"abstract_inverted_index":{"We":[0,105],"study":[1],"the":[2,77,92,116,120,128,148,152,162],"following":[3],"two":[4,149,163],"problems:":[5],"i)":[6],"Given":[7,49],"a":[8,43,50,55,100,124],"random":[9,18,51,56],"graph":[10,14,52],"$G_{n,":[11],"m}$":[12],"(a":[13],"drawn":[15],"uniformly":[16],"at":[17,137],"from":[19],"all":[20],"graphs":[21],"on":[22],"$n$":[23],"vertices":[24],"with":[25,34,54,72,127,158],"exactly":[26,85],"$m$":[27],"edges),":[28],"can":[29,67],"we":[30,68],"color":[31,40,69,81,97],"its":[32,59,70],"edges":[33,71],"$r$":[35,73],"colors":[36,74],"such":[37,94,123],"that":[38,79,95,107,147],"no":[39,96],"class":[41,98],"contains":[42,99],"component":[44,101],"of":[45,58,64,91,102,122,133],"size":[46,65,103],"$\\Theta(n)$?":[47,104],"ii)":[48],"$G_{n,m}$":[53],"partition":[57,93],"edge":[60,87],"set":[61,90],"into":[62],"sets":[63],"$r$,":[66],"subject":[75],"to":[76],"restriction":[78],"every":[80,89],"is":[82,136,155],"used":[83],"for":[84,108,119,131,139,161],"one":[86],"in":[88,113,156],"prove":[106],"any":[109],"fixed":[110],"$r\\geq":[111],"2$,":[112],"both":[114],"settings":[115],"(sharp)":[117],"threshold":[118,130,154],"existence":[121],"coloring":[125],"coincides":[126],"known":[129,159],"$r$-orientability":[132],"$G_{n,m}$,":[134],"which":[135],"$m=rc_r^*n$":[138],"some":[140],"analytically":[141],"computable":[142],"constant":[143],"$c_r^*$.":[144],"The":[145],"fact":[146],"problems":[150],"have":[151],"same":[153],"contrast":[157],"results":[160],"corresponding":[164],"Achlioptas-type":[165],"problems.":[166]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}