{"id":"https://openalex.org/W3108105039","doi":"https://doi.org/10.37236/10585","title":"Tight Bounds on Probabilistic Zero Forcing on Hypercubes and Grids","display_name":"Tight Bounds on Probabilistic Zero Forcing on Hypercubes and Grids","publication_year":2022,"publication_date":"2022-01-28","ids":{"openalex":"https://openalex.org/W3108105039","doi":"https://doi.org/10.37236/10585","mag":"3108105039"},"language":"en","primary_location":{"id":"doi:10.37236/10585","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10585","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p3/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":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p3/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036494857","display_name":"Natalie Behague","orcid":"https://orcid.org/0000-0001-6616-1606"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Natalie C. Behague","raw_affiliation_strings":["Ryerson University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ryerson University","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037471767","display_name":"Trent G. Marbach","orcid":"https://orcid.org/0000-0002-3708-3095"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Trent G. Marbach","raw_affiliation_strings":["Ryerson University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ryerson University","institution_ids":["https://openalex.org/I530967"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079925942","display_name":"Pawe\u0142 Pra\u0142at","orcid":"https://orcid.org/0000-0001-9176-8493"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Pawe\u0142 Pra\u0142at","raw_affiliation_strings":["Ryerson University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ryerson University","institution_ids":["https://openalex.org/I530967"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01069265,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9993000030517578,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9959999918937683,"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/T12288","display_name":"Optimization and Search Problems","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/hypercube","display_name":"Hypercube","score":0.7702243328094482},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6894473433494568},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.6457309722900391},{"id":"https://openalex.org/keywords/forcing","display_name":"Forcing (mathematics)","score":0.6144421100616455},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6017245054244995},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5218702554702759},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48870065808296204},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40260976552963257},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.09208700060844421},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08403754234313965}],"concepts":[{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.7702243328094482},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6894473433494568},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.6457309722900391},{"id":"https://openalex.org/C197115733","wikidata":"https://www.wikidata.org/wiki/Q1003136","display_name":"Forcing (mathematics)","level":2,"score":0.6144421100616455},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6017245054244995},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5218702554702759},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48870065808296204},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40260976552963257},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.09208700060844421},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08403754234313965},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.37236/10585","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10585","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p3/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"},{"id":"pmh:oai:arXiv.org:2012.00216","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2012.00216","pdf_url":"https://arxiv.org/pdf/2012.00216","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:3108105039","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2012.00216","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":"doi:10.48550/arxiv.2012.00216","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2012.00216","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.37236/10585","is_oa":true,"landing_page_url":"https://doi.org/10.37236/10585","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v29i1p3/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":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3108105039.pdf","grobid_xml":"https://content.openalex.org/works/W3108105039.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1767877588","https://openalex.org/W1968626979","https://openalex.org/W1996839950","https://openalex.org/W2099618798","https://openalex.org/W2101363765","https://openalex.org/W2120575449","https://openalex.org/W2141046366","https://openalex.org/W2245700130","https://openalex.org/W2336317531","https://openalex.org/W2474633304","https://openalex.org/W2908201806","https://openalex.org/W2909777159","https://openalex.org/W2954807575","https://openalex.org/W2963157019","https://openalex.org/W2964164538","https://openalex.org/W2964204801","https://openalex.org/W2973207532","https://openalex.org/W3034650401","https://openalex.org/W3144881883","https://openalex.org/W6642191556","https://openalex.org/W6678107996","https://openalex.org/W6681150932","https://openalex.org/W6721489647","https://openalex.org/W6738177336","https://openalex.org/W6767793264","https://openalex.org/W6788622076"],"related_works":["https://openalex.org/W110304795"],"abstract_inverted_index":{"Zero":[0],"forcing":[1,52,67],"is":[2],"a":[3,27,48],"deterministic":[4],"iterative":[5],"graph":[6],"colouring":[7],"process":[8],"in":[9,19],"which":[10],"vertices":[11,24,34,46],"are":[12],"coloured":[13],"either":[14],"blue":[15,23,45],"or":[16],"white,":[17],"and":[18,70],"every":[20],"round,":[21],"any":[22],"that":[25],"have":[26,47],"single":[28],"white":[29,33,54],"neighbour":[30,55],"force":[31],"these":[32],"to":[35,56],"become":[36,57],"blue.":[37,58],"Here":[38],"we":[39],"study":[40],"probabilistic":[41,65],"zero":[42,66],"forcing,":[43],"where":[44],"non-zero":[49],"probability":[50],"of":[51],"each":[53],"We":[59],"explore":[60],"the":[61],"propagation":[62],"time":[63],"for":[64],"on":[68],"hypercubes":[69],"grids.":[71]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}