{"id":"https://openalex.org/W2999914359","doi":"https://doi.org/10.37236/8113","title":"Saturation Games for Odd Cycles","display_name":"Saturation Games for Odd Cycles","publication_year":2019,"publication_date":"2019-10-11","ids":{"openalex":"https://openalex.org/W2999914359","doi":"https://doi.org/10.37236/8113","mag":"2999914359"},"language":"en","primary_location":{"id":"doi:10.37236/8113","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8113","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i4p11/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/v26i4p11/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005628569","display_name":"Sam Spiro","orcid":"https://orcid.org/0000-0001-5715-1940"},"institutions":[{"id":"https://openalex.org/I2800935791","display_name":"UC San Diego Health System","ror":"https://ror.org/01kbfgm16","country_code":"US","type":"healthcare","lineage":["https://openalex.org/I2800935791"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Sam Spiro","raw_affiliation_strings":["UC San Diego"],"affiliations":[{"raw_affiliation_string":"UC San Diego","institution_ids":["https://openalex.org/I2800935791"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5005628569"],"corresponding_institution_ids":["https://openalex.org/I2800935791"],"apc_list":null,"apc_paid":null,"fwci":0.5484,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.83664439,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"26","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9678000211715698,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T12137","display_name":"Economic theories and models","score":0.9678000211715698,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9584000110626221,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9409999847412109,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.843176007270813},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6195598244667053},{"id":"https://openalex.org/keywords/saturation","display_name":"Saturation (graph theory)","score":0.5974982380867004},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5584840774536133},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5125570297241211},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3366149067878723}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.843176007270813},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6195598244667053},{"id":"https://openalex.org/C9930424","wikidata":"https://www.wikidata.org/wiki/Q7426587","display_name":"Saturation (graph theory)","level":2,"score":0.5974982380867004},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5584840774536133},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5125570297241211},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3366149067878723},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/8113","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8113","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i4p11/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:10.37236/8113","is_oa":true,"landing_page_url":"https://doi.org/10.37236/8113","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i4p11/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/G2767563906","display_name":null,"funder_award_id":"DMS-1800746","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8388253343","display_name":"CAREER: Ramsey Theory and Discrete Geometry","funder_award_id":"1800746","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/W2999914359.pdf","grobid_xml":"https://content.openalex.org/works/W2999914359.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1882048990","https://openalex.org/W1986500264","https://openalex.org/W2056892547","https://openalex.org/W2073362670","https://openalex.org/W2606098847","https://openalex.org/W2963671784","https://openalex.org/W4301181796"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W1991411408","https://openalex.org/W4288278856","https://openalex.org/W2572370460"],"abstract_inverted_index":{"Given":[0],"a":[1,41,125],"family":[2],"of":[3,61,87,113,117,119,127,181],"graphs":[4],"$\\mathcal{F}$,":[5],"we":[6,164],"consider":[7,124],"the":[8,28,58,62,67,74,79,85,92,104,115,179],"$\\mathcal{F}$-saturation":[9],"game.":[10,80,129],"In":[11,160],"this":[12,128,163],"game,":[13],"two":[14],"players":[15,63,97],"alternate":[16],"adding":[17],"edges":[18,53,88],"to":[19,57,65,77,108,155,162],"an":[20,37],"initially":[21],"empty":[22],"graph":[23,94],"on":[24],"$n$":[25],"vertices,":[26],"with":[27,149],"only":[29],"constraint":[30],"being":[31],"that":[32,39,43,89,135,142],"neither":[33],"player":[34],"can":[35,54],"add":[36],"edge":[38],"creates":[40],"subgraph":[42],"lies":[44],"in":[45,91],"$\\mathcal{F}$.":[46],"The":[47,100],"game":[48,68,102,107],"ends":[49],"when":[50,95],"no":[51],"more":[52],"be":[55,109],"added":[56],"graph.":[59],"One":[60],"wishes":[64,76],"end":[66],"as":[69,71,112,157],"quickly":[70],"possible,":[72],"while":[73],"other":[75],"prolong":[78],"We":[81,123,133],"let":[82],"$\\textrm{sat}_g(\\mathcal{F};n)$":[83],"denote":[84],"number":[86],"are":[90],"final":[93],"both":[96],"play":[98],"optimally.&#x0D;":[99],"$\\{C_3\\}$-saturation":[101],"was":[103],"first":[105],"saturation":[106],"considered,":[110],"but":[111],"now":[114],"order":[116],"magnitude":[118],"$\\textrm{sat}_g(\\{C_3\\},n)$":[120],"remains":[121],"unknown.":[122],"variation":[126],"Let":[130],"$\\mathcal{C}_{2k+1}:=\\{C_3,\\":[131],"C_5,\\ldots,C_{2k+1}\\}$.":[132],"prove":[134,165],"$\\textrm{sat}_g(\\mathcal{C}_{2k+1};n)\\ge(\\frac{1}{4}-\\epsilon_k)n^2+o(n^2)$":[136],"for":[137,145,168],"all":[138,146,169,182],"$k\\ge":[139,147,170],"2$":[140],"and":[141,151,172],"$\\textrm{sat}_g(\\mathcal{C}_{2k+1};n)\\le":[143],"(\\frac{1}{4}-\\epsilon'_k)n^2+o(n^2)$":[144],"4$,":[148],"$\\epsilon_k&lt;\\frac{1}{4}$":[150],"$\\epsilon'_k&gt;0$":[152],"constants":[153],"tending":[154],"0":[156],"$k\\to":[158],"\\infty$.":[159],"addition":[161],"$\\textrm{sat}_g(\\{C_{2k+1}\\};n)\\le":[166],"\\frac{4}{27}n^2+o(n^2)$":[167],"2$,":[171],"$\\textrm{sat}_g(\\mathcal{C}_\\infty\\setminus":[173],"C_3;n)\\le":[174],"2n-2$,":[175],"where":[176],"$\\mathcal{C}_\\infty$":[177],"denotes":[178],"set":[180],"odd":[183],"cycles.":[184]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
