{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:24:08Z","timestamp":1753885448536,"version":"3.41.2"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"name":"Basic Research Grant, BUET, Bangladesh","award":["applicable"],"award-info":[{"award-number":["applicable"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p> A bar visibility representation of a graph [Formula: see text] is an assignment of the vertices of [Formula: see text] to distinct horizontal line segments in the plane so that two vertices are adjacent in [Formula: see text] if and only if there is an uninterrupted vertical channel of positive width that joins the bars corresponding to those vertices. A bar visibility representation is called a unit bar visibility representation if every bar has the same length. If each vertex is assigned to [Formula: see text] distinct bars of the same length in a unit bar visibility representation then the representation is called [Formula: see text]-unit bar visibility representation. In this paper, we introduce a \u201csliding column model\u201d for [Formula: see text]-unit bar visibility representation and show that every graph of maximum degree [Formula: see text] has a [Formula: see text]-unit bar visibility representation for [Formula: see text]. We also show that a planar graph of maximum degree 3 having [Formula: see text] vertices and [Formula: see text] edges has a 2-unit bar visibility representation on [Formula: see text] columns and a 3-connected cubic graph of [Formula: see text] vertices admits a 2-unit bar visibility representation on [Formula: see text] columns. <\/jats:p>","DOI":"10.1142\/s1793830922501373","type":"journal-article","created":{"date-parts":[[2022,8,17]],"date-time":"2022-08-17T04:19:30Z","timestamp":1660709970000},"source":"Crossref","is-referenced-by-count":0,"title":["Sliding column model for t-unit bar visibility representations of graphs"],"prefix":"10.1142","volume":"15","author":[{"given":"Md. Manzurul","family":"Hasan","sequence":"first","affiliation":[{"name":"Graph Drawing & Information Visualization Laboratory, Department of Computer Science and Engineering (CSE), Bangladesh University of Engineering and Technology (BUET), Bangladesh"},{"name":"Department of Computer Science, American International University-Bangladesh (AIUB), Bangladesh"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9385-6315","authenticated-orcid":false,"given":"Shaheena","family":"Sultana","sequence":"additional","affiliation":[{"name":"Graph Drawing & Information Visualization Laboratory, Department of Computer Science and Engineering (CSE), Bangladesh University of Engineering and Technology (BUET), Bangladesh"},{"name":"Department of CSE, Notre Dame University Bangladesh (NDUB), Bangladesh"}]},{"given":"Md. 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