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Paper Abstract and Keywords
Presentation 2006-10-17 09:00
Convex Grid Drawings of Plane Graphs with Rectangular Contours
Akira Kamada (Tohoku Univ.), Kazuyuki Miura (Fukushima Univ.), Takao Nishizeki (Tohoku Univ.)
Abstract (in Japanese) (See Japanese page) 
(in English) In a convex drawing of a plane graph, all edges are drawn as straight-line segments without any edge-intersection and all facial cycles are drawn as convex polygons.
In a convex grid drawing, all vertices are put on grid points.
A plane graph $G$ has a convex drawing if and only if $G$ is internally triconnected,and an internally triconnected plane graph $G$ has a convex grid drawing on an $n \times n$ grid if $G$ is triconnected or the triconnected component decomposition tree $T(G)$ of $G$ has two or three leaves, where $n$ is the number of vertices in $G$.
In this paper, we show that an internally triconnected plane graph $G$ has a convex grid drawing on a $2n \times n^2$ grid if $T(G)$ has exactly four leaves.
We also present an algorithm to find such a drawing in linear time.
Our convex grid drawing has a rectangular contour, while most of the known algorithms produce grid drawings having triangular contours.
Keyword (in Japanese) (See Japanese page) 
(in English) algorithm / convex grid drawing / graph drawing / plane graph / triconnected / / /  
Reference Info. IEICE Tech. Rep., vol. 106, no. 289, COMP2006-31, pp. 1-8, Oct. 2006.
Paper # COMP2006-31 
Date of Issue 2006-10-10 (COMP) 
ISSN Print edition: ISSN 0913-5685
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Conference Information
Committee COMP  
Conference Date 2006-10-17 - 2006-10-17 
Place (in Japanese) (See Japanese page) 
Place (in English) Tohoku University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2006-10-COMP 
Language English (Japanese title is available) 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Convex Grid Drawings of Plane Graphs with Rectangular Contours 
Sub Title (in English)  
Keyword(1) algorithm  
Keyword(2) convex grid drawing  
Keyword(3) graph drawing  
Keyword(4) plane graph  
Keyword(5) triconnected  
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1st Author's Name Akira Kamada  
1st Author's Affiliation Tohoku University (Tohoku Univ.)
2nd Author's Name Kazuyuki Miura  
2nd Author's Affiliation Fukushima University (Fukushima Univ.)
3rd Author's Name Takao Nishizeki  
3rd Author's Affiliation Tohoku University (Tohoku Univ.)
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Speaker Author-1 
Date Time 2006-10-17 09:00:00 
Presentation Time 35 minutes 
Registration for COMP 
Paper # COMP2006-31 
Volume (vol) vol.106 
Number (no) no.289 
Page pp.1-8 
#Pages
Date of Issue 2006-10-10 (COMP) 


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