{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:55:10Z","timestamp":1787324110165,"version":"build-2736575974"},"reference-count":25,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1440140"],"award-info":[{"award-number":["DMS-1440140"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Discrete Math."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>We prove that if $G$ is a graph without 3-cycles and 4-cycles, then the discrete cubical homology of $G$ is trivial in dimension $d$ for all $d\\ge 2$. We also construct a sequence $\\{G_d\\}$ of graphs such that this homology is nontrivial in dimension $d$ for $d\\ge 1$. Finally, we show that the discrete cubical homology induced by certain coverings of $G$ equals the ordinary singular homology of a $2$-dimensional cell complex built from $G$, although in general it differs from the discrete cubical homology of the graph as a whole.<\/jats:p>","DOI":"10.1137\/20m1338484","type":"journal-article","created":{"date-parts":[[2021,1,7]],"date-time":"2021-01-07T12:28:11Z","timestamp":1610022491000},"page":"35-54","source":"Crossref","is-referenced-by-count":2,"title":["On the Vanishing of Discrete Singular Cubical Homology for Graphs"],"prefix":"10.1137","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9248-1232","authenticated-orcid":true,"given":"H\u00e9l\u00e8ne","family":"Barcelo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Curtis","family":"Greene","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Abdul Salam","family":"Jarrah","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Volkmar","family":"Welker","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,1,7]]},"reference":[{"key":"atypb1","first-page":"82","author":"Angluin D.","year":"1980","journal-title":"New York"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-7373(74)80024-6"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-7373(76)80015-6"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s10801-006-9100-0"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1112\/blms\/bdu043"},{"key":"atypb6","first-page":"417","volume":"2","author":"Barcelo H.","year":"2019","journal-title":"Algebr. Comb."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1006\/aama.2000.0710"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2011-05336-5"},{"key":"atypb9","first-page":"1819","author":"Bj\u00f6rner A.","year":"1996","journal-title":"MA"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"M. Bridson and A. Haefliger,\n                      Metric Spaces of Non-Positive Curvature\n                      , Springer, Berlin, 1999,https:\/\/doi.org\/10.1007\/978-3-662-12494-9.","DOI":"10.1007\/978-3-662-12494-9"},{"key":"atypb11","doi-asserted-by":"crossref","unstructured":"K. S. Brown,\n                      Cohomology of Groups\n                      , Grad. Texts in Math. 87, Springer, New York, 1982.","DOI":"10.1007\/978-1-4684-9327-6"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1017\/prm.2018.102"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"R. Diestel,\n                      Graph Theory\n                      , Grad. Texts Math. 173, Springer, New York, 2000,https:\/\/doi.org\/10.1007\/978-3-662-53622-3.","DOI":"10.1007\/978-3-662-53622-3_7"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.4310\/PAMQ.2014.v10.n4.a2"},{"key":"atypb15","unstructured":"R. Hardeman,\n                      Computing A-Homotopy Groups using Coverings and Lifting Properties\n                      , Master's thesis, University of Calgary, Calgary, Canada, 2018."},{"key":"atypb16","unstructured":"A. Hatcher,\n                      Algebraic Topology\n                      , Cambridge University Press, Reading, MA, 2013."},{"key":"atypb17","unstructured":"M. Kraetzl, R. Laubenbacher, and M. Gaston,\n                      Combinatorial and Algebraic Approaches to Network Analysis\n                      , DSTO Internal Report, 2001."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(82)90042-9"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01896190"},{"key":"atypb20","doi-asserted-by":"crossref","unstructured":"W. Massey,\n                      A Basic Course in Algebraic Topology\n                      , Grad. Texts in Math. 127, Springer, New York, 1991,https:\/\/doi.org\/10.1007\/978-1-4939-9063-4.","DOI":"10.1007\/978-1-4939-9063-4"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(73)90005-1"},{"key":"atypb22","unstructured":"J. Munkres,\n                      Elements of Algebraic Topology\n                      , Addison-Wesley, Reading, MA, 1984."},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"T. Sunada,\n                      Topological Crystallography\n                      , Surv. Tutor. Appl. Math. Sci. 91, Springer, Tokyo, 2013,https:\/\/doi.org\/10.1007\/978-4-431-54177-6.","DOI":"10.1007\/978-4-431-54177-6"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1112\/blms.12187"},{"key":"atypb25","doi-asserted-by":"crossref","unstructured":"C. A. Weibel,\n                      Introduction to Homological Algebra\n                      , Cambridge University Press, Cambridge, 1994,https:\/\/doi.org\/10.1017\/CBO9781139644136.","DOI":"10.1017\/CBO9781139644136"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/20M1338484","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:18:51Z","timestamp":1787321931000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/20M1338484"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/20M1338484"],"URL":"https:\/\/doi.org\/10.1137\/20m1338484","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}