{"id":"https://openalex.org/W2971878942","doi":"https://doi.org/10.1137/20m1338484","title":"On the Vanishing of Discrete Singular Cubical Homology for Graphs","display_name":"On the Vanishing of Discrete Singular Cubical Homology for Graphs","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W2971878942","doi":"https://doi.org/10.1137/20m1338484","mag":"2971878942"},"language":"en","primary_location":{"id":"doi:10.1137/20m1338484","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1338484","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1909.02901","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050021092","display_name":"H\u00e9l\u00e8ne Barcelo","orcid":"https://orcid.org/0000-0001-9248-1232"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"H\u00e9l\u00e8ne Barcelo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103679717","display_name":"Curtis Greene","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Curtis Greene","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083154892","display_name":"Abdul Salam Jarrah","orcid":"https://orcid.org/0000-0001-6771-2561"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abdul Salam Jarrah","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5006798935","display_name":"Volkmar Welker","orcid":"https://orcid.org/0000-0002-6892-5427"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Volkmar Welker","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5050021092"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1515,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.4631099,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"35","issue":"1","first_page":"35","last_page":"54"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":1.0,"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/T10896","display_name":"Homotopy and Cohomology in Algebraic Topology","score":0.9962000250816345,"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/T10086","display_name":"Alzheimer's disease research and treatments","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2737","display_name":"Physiology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homology","display_name":"Homology (biology)","score":0.7336583733558655},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7173031568527222},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5514562726020813},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.48970940709114075},{"id":"https://openalex.org/keywords/singular-homology","display_name":"Singular homology","score":0.4691442549228668},{"id":"https://openalex.org/keywords/cellular-homology","display_name":"Cellular homology","score":0.4101468324661255},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36311256885528564},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35451751947402954},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.19867244362831116},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.05950427055358887},{"id":"https://openalex.org/keywords/genetics","display_name":"Genetics","score":0.046733081340789795}],"concepts":[{"id":"https://openalex.org/C165525559","wikidata":"https://www.wikidata.org/wiki/Q224180","display_name":"Homology (biology)","level":3,"score":0.7336583733558655},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7173031568527222},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5514562726020813},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.48970940709114075},{"id":"https://openalex.org/C139962677","wikidata":"https://www.wikidata.org/wiki/Q1095056","display_name":"Singular homology","level":3,"score":0.4691442549228668},{"id":"https://openalex.org/C55537702","wikidata":"https://www.wikidata.org/wiki/Q3139849","display_name":"Cellular homology","level":3,"score":0.4101468324661255},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36311256885528564},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35451751947402954},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.19867244362831116},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.05950427055358887},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.046733081340789795},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/20m1338484","is_oa":false,"landing_page_url":"https://doi.org/10.1137/20m1338484","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"},{"id":"pmh:oai:arXiv.org:1909.02901","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.02901","pdf_url":"https://arxiv.org/pdf/1909.02901","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:2971878942","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1909.02901.pdf","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.1909.02901","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.02901","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1909.02901","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.02901","pdf_url":"https://arxiv.org/pdf/1909.02901","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"},"sustainable_development_goals":[{"score":0.5699999928474426,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G1211463696","display_name":null,"funder_award_id":"144014","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4402292705","display_name":null,"funder_award_id":"DMS-1440140","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G811546825","display_name":null,"funder_award_id":"1440140","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2971878942.pdf","grobid_xml":"https://content.openalex.org/works/W2971878942.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1496383623","https://openalex.org/W1535866048","https://openalex.org/W1971869754","https://openalex.org/W2010602879","https://openalex.org/W2028891720","https://openalex.org/W2049550828","https://openalex.org/W2077744016","https://openalex.org/W2079943001","https://openalex.org/W2083409154","https://openalex.org/W2153767444","https://openalex.org/W2163137233","https://openalex.org/W2579699847","https://openalex.org/W2741914562","https://openalex.org/W2765918107","https://openalex.org/W2923257707","https://openalex.org/W2941918431","https://openalex.org/W2962796441","https://openalex.org/W2963142861","https://openalex.org/W3101241802","https://openalex.org/W3124646649","https://openalex.org/W3141871949","https://openalex.org/W4250764680"],"related_works":["https://openalex.org/W3119444938","https://openalex.org/W2953577858","https://openalex.org/W2963142861","https://openalex.org/W3088796972","https://openalex.org/W1943640941","https://openalex.org/W1554025500","https://openalex.org/W3101241802","https://openalex.org/W3149541006","https://openalex.org/W1959979995","https://openalex.org/W2223894580","https://openalex.org/W2000116379","https://openalex.org/W3161782078","https://openalex.org/W2287887107","https://openalex.org/W287883068","https://openalex.org/W2779325793","https://openalex.org/W2951780434","https://openalex.org/W2952476048","https://openalex.org/W2563975616","https://openalex.org/W3163619504","https://openalex.org/W2012300380"],"abstract_inverted_index":{"We":[0,28],"prove":[1],"that":[2,37,51],"if":[3],"$G$":[4,18,61],"is":[5,19,40],"a":[6,31,68,89],"graph":[7,87],"without":[8],"3-cycles":[9],"and":[10],"4-cycles,":[11],"then":[12],"the":[13,52,63,81,86],"discrete":[14,53,82],"cubical":[15,54,83],"homology":[16,39,55,66,84],"of":[17,34,60,67,85],"trivial":[20],"in":[21,42,76],"dimension":[22,43],"$d$":[23,44],"for":[24,45],"all":[25],"$d\\ge":[26,46],"2$.":[27],"also":[29],"construct":[30],"sequence":[32],"$\\{G_d\\}$":[33],"graphs":[35],"such":[36],"this":[38],"nontrivial":[41],"1$.":[47],"Finally,":[48],"we":[49],"show":[50],"induced":[56],"by":[57],"certain":[58],"coverings":[59],"equals":[62],"ordinary":[64],"singular":[65],"$2$-dimensional":[69],"cell":[70],"complex":[71],"built":[72],"from":[73,80],"$G$,":[74],"although":[75],"general":[77],"it":[78],"differs":[79],"as":[88],"whole.":[90]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
