{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:45:28Z","timestamp":1787323528367,"version":"build-2736575974"},"reference-count":18,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NSFC-11871439"],"award-info":[{"award-number":["NSFC-11871439"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["NSFC-11401430"],"award-info":[{"award-number":["NSFC-11401430"]}],"id":[{"id":"10.13039\/501100001809","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>A $t$-bar visibility representation of a graph assigns each vertex up to $t$ horizontal bars in the plane so that two vertices are adjacent if and only if some bar for one vertex can see some bar for the other via an unobstructed vertical channel of positive width. The least $t$ such that $G$ has a $t$-bar visibility representation is the bar visibility number of $G$, denoted by $b(G)$. For the complete bipartite graph $K_{m,n}$, the lower bound $b(K_{m,n})\\ge\\lceil{\\frac{mn+4}{2m+2n}}\\rceil$ from Euler's formula is well known. We prove that equality holds.<\/jats:p>","DOI":"10.1137\/19m1260268","type":"journal-article","created":{"date-parts":[[2021,9,28]],"date-time":"2021-09-28T12:12:50Z","timestamp":1632831170000},"page":"2234-2248","source":"Crossref","is-referenced-by-count":0,"title":["On the Bar Visibility Number of Complete Bipartite Graphs"],"prefix":"10.1137","volume":"35","author":[{"given":"Weiting","family":"Cao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Douglas B.","family":"West","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,9,28]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/120864234"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1968-088-x"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100037385"},{"key":"atypb4","unstructured":"W. Cao,\n                      Some Problems in Structural Graph Theory\n                      , Ph.D. Thesis, University of Illinois, Urbana-Champaign, IL, 2006."},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480198343455"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-2016-020-1"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-017-0328-y"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2020.01.011"},{"key":"atypb9","doi-asserted-by":"crossref","unstructured":"S.K. Ghosh, Visibility Algorithms in the Plane, Cambridge University Press, Cambridge, 2007.","DOI":"10.1017\/CBO9780511543340"},{"key":"atypb10","first-page":"332","volume":"24","author":"Heawood P.J.","year":"1890","journal-title":"Q. J. Math"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.6028\/jres.072B.018"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2004.12.004"},{"key":"atypb13","first-page":"146","volume":"347","author":"Ringel G.","year":"1984","journal-title":"J. Reine Angew. Math."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1007\/BF02187705"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(98)00110-1"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-016-1745-4"},{"key":"atypb17","first-page":"147","author":"Wismath S.","year":"1985","journal-title":"New York"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2018.02.024"}],"container-title":["SIAM Journal on Discrete Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/19M1260268","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:07:32Z","timestamp":1787321252000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/19M1260268"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1137\/19M1260268"],"URL":"https:\/\/doi.org\/10.1137\/19m1260268","relation":{},"ISSN":["0895-4801","1095-7146"],"issn-type":[{"value":"0895-4801","type":"print"},{"value":"1095-7146","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]}}}