Abstract
It is important to minimize the area of a drawing of a graph, so that the drawing can fit in a small drawing-space. It is well-known that a planar graph with n vertices admits a planar straight-line grid drawing with O ( n 2 ) area [H. de Fraysseix, J. Pach, R. Pollack, How to draw a planar graph on a grid, Combinatorica 10(1) (1990) 41–51; W. Schnyder, Embedding planar graphs on the grid, in: Proceedings of the First ACM-SIAM Symposium on Discrete Algorithms, 1990, pp. 138–148]. Unfortunately, there is a matching lower-bound of Ω ( n 2 ) on the area-requirements of the planar straight-line grid drawings of certain planar graphs. Hence, it is important to investigate important categories of planar graphs to determine if they admit planar straight-line grid drawings with o ( n 2 ) area. In this paper, we investigate an important category of planar graphs, namely, outerplanar graphs. We show that an outerplanar graph G with degree d admits a planar straight-line grid drawing with area O ( dn 1.48 ) in O ( n ) time. This implies that if d = o ( n 0.52 ) , then G can be drawn in this manner in o ( n 2 ) area.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
