{"id":"https://openalex.org/W3005046498","doi":"https://doi.org/10.1017/s0963548319000452","title":"On subgraphs of <i>C</i><sub>2<i>k</i></sub>-free graphs and a problem of K\u00fchn and Osthus","display_name":"On subgraphs of <i>C</i><sub>2<i>k</i></sub>-free graphs and a problem of K\u00fchn and Osthus","publication_year":2020,"publication_date":"2020-02-04","ids":{"openalex":"https://openalex.org/W3005046498","doi":"https://doi.org/10.1017/s0963548319000452","mag":"3005046498"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548319000452","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548319000452","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5084371772","display_name":"D\u00e1niel Gr\u00f3sz","orcid":"https://orcid.org/0000-0001-8817-1346"},"institutions":[{"id":"https://openalex.org/I108290504","display_name":"University of Pisa","ror":"https://ror.org/03ad39j10","country_code":"IT","type":"education","lineage":["https://openalex.org/I108290504"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"D\u00e1niel Gr\u00f3sz","raw_affiliation_strings":["Department of Mathematics, University of Pisa, 56127Pisa, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Pisa, 56127Pisa, Italy","institution_ids":["https://openalex.org/I108290504"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041720529","display_name":"Abhishek Methuku","orcid":"https://orcid.org/0000-0002-5244-5365"},"institutions":[{"id":"https://openalex.org/I4210104335","display_name":"Institute for Basic Science","ror":"https://ror.org/00y0zf565","country_code":"KR","type":"facility","lineage":["https://openalex.org/I4210104335"]},{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH","KR"],"is_corresponding":false,"raw_author_name":"Abhishek Methuku","raw_affiliation_strings":["\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland, and Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne, Switzerland, and Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, Republic of Korea","institution_ids":["https://openalex.org/I5124864","https://openalex.org/I4210104335"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018137609","display_name":"Casey Tompkins","orcid":"https://orcid.org/0000-0003-2618-0604"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":true,"raw_author_name":"Casey Tompkins","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, 1053 Hungary Karlsruhe Institute of Technology, 76131Karlsruhe, Germany, and Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, Republic of Korea"],"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, 1053 Hungary Karlsruhe Institute of Technology, 76131Karlsruhe, Germany, and Discrete Mathematics Group, Institute for Basic Science (IBS), Daejeon, Republic of Korea","institution_ids":["https://openalex.org/I127817813"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018137609","https://openalex.org/A5084371772"],"corresponding_institution_ids":["https://openalex.org/I108290504","https://openalex.org/I127817813"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.13618802,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"3","first_page":"436","last_page":"454"},"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":0.9998999834060669,"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":0.9998999834060669,"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":0.9937999844551086,"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/T11476","display_name":"Graph theory and applications","score":0.955299973487854,"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":0.8441586494445801},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.7990509271621704},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7252305150032043},{"id":"https://openalex.org/keywords/hypergraph","display_name":"Hypergraph","score":0.6211722493171692},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4539007544517517},{"id":"https://openalex.org/keywords/complete-bipartite-graph","display_name":"Complete bipartite graph","score":0.4385172724723816},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.41139188408851624},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36309754848480225},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.059975236654281616}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8441586494445801},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.7990509271621704},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7252305150032043},{"id":"https://openalex.org/C2781221856","wikidata":"https://www.wikidata.org/wiki/Q840247","display_name":"Hypergraph","level":2,"score":0.6211722493171692},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4539007544517517},{"id":"https://openalex.org/C134119311","wikidata":"https://www.wikidata.org/wiki/Q913598","display_name":"Complete bipartite graph","level":4,"score":0.4385172724723816},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.41139188408851624},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36309754848480225},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.059975236654281616},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0963548319000452","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548319000452","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1971010887","https://openalex.org/W1994460648","https://openalex.org/W1997059040","https://openalex.org/W2021022635","https://openalex.org/W2021817919","https://openalex.org/W2052325621","https://openalex.org/W2065796538","https://openalex.org/W2103012681","https://openalex.org/W2110805362","https://openalex.org/W2330868067","https://openalex.org/W2336338640","https://openalex.org/W2528403005","https://openalex.org/W4233413206","https://openalex.org/W4250699352"],"related_works":["https://openalex.org/W2091826982","https://openalex.org/W2036057584","https://openalex.org/W2107875203","https://openalex.org/W245205139","https://openalex.org/W4234658180","https://openalex.org/W4235849992","https://openalex.org/W4246000090","https://openalex.org/W2910933086","https://openalex.org/W4288630335","https://openalex.org/W3143578817"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"c":[2,26,40,46],"denote":[3],"the":[4,94,127,137,193,249],"largest":[5],"constant":[6],"such":[7],"that":[8,37,45,53,225],"every":[9,226],"C":[10,19,68,103,116,228,236,264,273],"6":[11],"-free":[12,21,71,106,118,231,238,267],"graph":[13,72,107,232],"G":[14,30,233,252],"contains":[15,234],"a":[16,24,67,78,90,102,113,123,147,159,169,189,210,217,235,243,257],"bipartite":[17,79,114,227],"and":[18,34,59,115,156,212,221,261],"4":[20,117,237],"subgraph":[22,80,119,239],"having":[23],"fraction":[25,91,124,190,244],"of":[27,29,81,93,96,126,129,133,149,173,192,195,203,216,219,248,251,259],"edges":[28,95,128,250],".":[31,98,131,197,253],"Gy\u0151ri,":[32],"Kensell":[33],"Tompkins":[35],"showed":[36],"3/8":[38],"\u2a7d":[39,41],"2/5.":[42],"We":[43,198,254],"prove":[44,142,200],"=":[47],"38.":[48],"More":[49],"generally,":[50],"we":[51,141,208],"show":[52],"for":[54],"any":[55,60,152,157,182],"\u03b5":[56,153],"&gt;":[57,154,279],"0,":[58,155],"integer":[61],"k":[62,70,86,105,163,177,230,246,266,278],"\u2a7e":[63,164,281],"2,":[64,165],"there":[65,166],"is":[66],"2":[69,85,104,229,265,274],"$G'$":[73,97],"which":[74,109,140,178,223],"does":[75,110,179],"not":[76,111,180],"contain":[77,112,181],"girth":[82,174],"greater":[83,175],"than":[84,89,122,176,188],"with":[87,120,186,240],"more":[88,121,187],"$$\\Bigl(1-\\frac{1}{2^{2k-2}}\\Bigr)\\frac{2}{2k-1}(1+\\varepsilon)$$":[92],"There":[99],"also":[100,199,255],"exists":[101,167],"$G''$":[108,130],"$$\\Bigl(1-\\frac{1}{2^{k-1}}\\Bigr)\\frac{1}{k-1}(1+\\varepsilon)$$":[125],"One":[132],"our":[134],"proofs":[135],"uses":[136],"following":[138],"statement,":[139],"using":[143],"probabilistic":[144],"ideas,":[145],"generalizing":[146],"theorem":[148],"Erd\u0151s.":[150],"For":[151],"integers":[158],",":[160,162],"b":[161,183],"an":[168],"-uniform":[170],"hypergraph":[171],"H":[172,196],"-colourable":[184],"subhypergraph":[185],"$$\\Bigl(1-\\frac{1}{b^{a-1}}\\Bigr)(1+\\varepsilon)$$":[191],"hyperedges":[194],"further":[201],"generalizations":[202],"this":[204],"theorem.":[205],"In":[206],"addition,":[207],"give":[209],"new":[211],"very":[213],"short":[214],"proof":[215],"result":[218],"K\u00fchn":[220,260],"Osthus,":[222],"states":[224],"at":[241],"least":[242],"1/(":[245],"\u22121)":[247],"answer":[256],"question":[258],"Osthus":[262],"about":[263],"graphs":[268],"obtained":[269],"by":[270],"pasting":[271],"together":[272],"l":[275,280],"\u2019s":[276],"(with":[277],"3).":[282]},"counts_by_year":[],"updated_date":"2026-01-15T23:16:33.117629","created_date":"2020-02-14T00:00:00"}
