{"id":"https://openalex.org/W4376611037","doi":"https://doi.org/10.1137/22m1471365","title":"On Connected Components with Many Edges","display_name":"On Connected Components with Many Edges","publication_year":2023,"publication_date":"2023-05-15","ids":{"openalex":"https://openalex.org/W4376611037","doi":"https://doi.org/10.1137/22m1471365"},"language":"en","primary_location":{"id":"doi:10.1137/22m1471365","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1471365","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":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000121525","display_name":"Sammy Luo","orcid":"https://orcid.org/0000-0002-4618-5472"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sammy Luo","raw_affiliation_strings":["Department of Mathematics, Stanford University, Stanford, CA 94305 USA"],"raw_orcid":"https://orcid.org/0000-0002-4618-5472","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Stanford University, Stanford, CA 94305 USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000121525"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":2.0087,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.83322215,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"37","issue":"2","first_page":"573","last_page":"585"},"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":0.9941999912261963,"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":0.9941999912261963,"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":0.9927999973297119,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9114000201225281,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8150132894515991},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8133195042610168},{"id":"https://openalex.org/keywords/monochromatic-color","display_name":"Monochromatic color","score":0.8014272451400757},{"id":"https://openalex.org/keywords/multipartite","display_name":"Multipartite","score":0.7031860947608948},{"id":"https://openalex.org/keywords/graph-factorization","display_name":"Graph factorization","score":0.692797064781189},{"id":"https://openalex.org/keywords/connected-component","display_name":"Connected component","score":0.691119372844696},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.6537333726882935},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5146521329879761},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46558940410614014},{"id":"https://openalex.org/keywords/edge-coloring","display_name":"Edge coloring","score":0.4490552246570587},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.439997136592865},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.22712549567222595},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.18556275963783264}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8150132894515991},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8133195042610168},{"id":"https://openalex.org/C40833965","wikidata":"https://www.wikidata.org/wiki/Q6901438","display_name":"Monochromatic color","level":2,"score":0.8014272451400757},{"id":"https://openalex.org/C166733315","wikidata":"https://www.wikidata.org/wiki/Q6934831","display_name":"Multipartite","level":4,"score":0.7031860947608948},{"id":"https://openalex.org/C128115575","wikidata":"https://www.wikidata.org/wiki/Q5597083","display_name":"Graph factorization","level":5,"score":0.692797064781189},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.691119372844696},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6537333726882935},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5146521329879761},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46558940410614014},{"id":"https://openalex.org/C123809776","wikidata":"https://www.wikidata.org/wiki/Q1050972","display_name":"Edge coloring","level":5,"score":0.4490552246570587},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.439997136592865},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.22712549567222595},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.18556275963783264},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C60644358","wikidata":"https://www.wikidata.org/wiki/Q128570","display_name":"Bioinformatics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1471365","is_oa":false,"landing_page_url":"https://doi.org/10.1137/22m1471365","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2499887605","display_name":null,"funder_award_id":"DGE-1656518","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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W78420916","https://openalex.org/W1524433708","https://openalex.org/W2752166164","https://openalex.org/W2986426282","https://openalex.org/W3196967814","https://openalex.org/W3198511689"],"related_works":["https://openalex.org/W2285156954","https://openalex.org/W2496154651","https://openalex.org/W4376611037","https://openalex.org/W4380551467","https://openalex.org/W398688634","https://openalex.org/W2359530226","https://openalex.org/W2242678273","https://openalex.org/W2357418035","https://openalex.org/W2380525562","https://openalex.org/W4291316360"],"abstract_inverted_index":{".We":[0],"prove":[1,30],"that":[2,31,56,86],"if":[3],"\\(H\\)":[4,16],"is":[5],"a":[6,9,18,38,42,58,61,65,73,96],"subgraph":[7,45,99],"of":[8,34,37,50,68,75,90,93],"complete":[10,39],"multipartite":[11],"graph":[12,40],"\\(G\\)":[13],",":[14,83],"then":[15],"contains":[17,41,95],"connected":[19,44,98],"component":[20],"\\(H'\\)":[21],"satisfying":[22],"\\(|E(H')||E(G)|\\geq":[23],"|E(H)|^2\\)":[24],".":[25],"We":[26,53],"use":[27],"this":[28],"to":[29],"every":[32,87],"3-coloring":[33],"the":[35,51,69,91],"edges":[36,92],"monochromatic":[43,62,97],"with":[46,64,100],"at":[47,101],"least":[48,102],"\\(1/6\\)":[49],"edges.":[52,70],"further":[54],"show":[55,85],"such":[57],"coloring":[59],"has":[60],"circuit":[63],"fraction":[66],"\\(1/6-o(1)\\)":[67],"This":[71],"verifies":[72],"conjecture":[74],"Conlon":[76],"and":[77],"Tyomkyn.":[78],"Moreover,":[79],"for":[80],"general":[81],"\\(k\\)":[82,88],"we":[84],"-coloring":[89],"\\(K_n\\)":[94],"\\(\\frac{1}{k^2-k+\\frac{5}{4}}\\binom{n}{2}\\)":[103],"edges.Keywordsconnected":[104],"componentsgraph":[105],"coloringRamsey":[106],"theoryMSC":[107],"codes05C1505C3505C4005C55":[108]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}