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dc.contributor.authorMd. Manzurul Hasan, Debajyoti Mondal, and Md. Saidur Rahman-
dc.date.accessioned2024-06-06T09:47:25Z-
dc.date.available2024-06-06T09:47:25Z-
dc.date.issued2024-01-30-
dc.identifier.urihttp://dspace.aiub.edu:8080/jspui/handle/123456789/2190-
dc.description.abstractA graph is called planar if it admits a planar drawing on the plane, i.e., no two edges create a crossing except possibly at their common endpoint. In a rectilinear drawing Γ of a planar graph, each vertex is drawn as a point and each edge is drawn as either horizontal or vertical line segment. A face in Γ is called orthogonally convex if every horizontal or vertical line segment connecting two points within the face does not intersect any other face. We examine the decision problem that takes a planar graph as an input and seeks for a rectilinear drawing where the faces are drawn as orthogonally convex polygons. A linear-time algorithm for this problem is known for biconnected planar graphs, but the algorithm relies on complex data structures and linear-time planarity testing, which are challenging to implement. In this paper, we give a necessary and sufficient condition for a subdivision of a triconnected cubic planar graph to admit such a drawing, and design a linear-time algorithm to check the condition and compute a desired drawing, if it exists. As a byproduct of our results we show that if a subdivision of a triconnected cubic planar graph G admits a rectilinear drawing, then it must also admit a rectilinear drawing with orthogonally convex faces.en_US
dc.description.sponsorshipsupported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART). © 2024 by the Mathematical Association of Thailanden_US
dc.publisherThai Journal of Mathematics -TJM (supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART)). © 2024 by the Mathematical Association of Thailanden_US
dc.subjectgraph drawing; rectilinear drawing; orthogonally convex face; subdivisionen_US
dc.titleLinear-Time Rectilinear Drawings of Subdivisions of Triconnected Cubic Planar Graphs with Orthogonally Convex Facesen_US
dc.typeArticleen_US
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