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APVIS
2007

Straight-line grid drawings of planar graphs with linear area

8 years 9 months ago
Straight-line grid drawings of planar graphs with linear area
A straight-line grid drawing of a planar graph G is a drawing of G on an integer grid such that each vertex is drawn as a grid point and each edge is drawn as a straight-line segment without edge crossings. It is well known that a planar graph of n vertices admits a straight-line grid drawing on a grid of area O(n2). A lower bound of Ω(n2) on the area-requirement for straight-line grid drawings of certain planar graphs are also known. In this paper, we introduce a fairly large class of planar graphs which admits a straightline grid drawing on a grid of area O(n). Our new class of planar graphs, which we call “doughnut graphs,” is a subclass of 5-connected planar graphs. We also show several interesting properties of “doughnut graphs” in this paper.
Md. Rezaul Karim, Md. Saidur Rahman
Added 29 Oct 2010
Updated 29 Oct 2010
Type Conference
Year 2007
Where APVIS
Authors Md. Rezaul Karim, Md. Saidur Rahman
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