IEICE TRANSACTIONS on Fundamentals
Convex Grid Drawings of Plane Graphs with Pentagonal Contours on O(n2) Grids
Summary :
In a convex grid drawing of a plane graph, all edges are drawn as straight-line segments without any edge-intersection, all vertices are put on grid points and all facial cycles are drawn as convex polygons. 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-1)×(n-1) grid if either 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. An internally triconnected plane graph G has a convex grid drawing on a 2n×2n grid if T(G) has exactly four leaves. Furthermore, an internally triconnected plane graph G has a convex grid drawing on a 6n×n2 grid if T(G) has exactly five leaves. In this paper, we show that an internally triconnected plane graph G has a convex grid drawing on a 20n×16n grid if T(G) has exactly five leaves. We also present an algorithm to find such a drawing in linear time. This is the first algorithm that finds a convex grid drawing of such a plane graph G in a grid of O(n2) size.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.9 pp.1142-1149
- Publication Date
- 2021/09/01
- Publicized
- 2021/03/10
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2020DMP0011
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
- Graphs and Networks
Authors
Kei SATO
Fukushima University
Kazuyuki MIURA
Fukushima University
Keyword
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Kei SATO, Kazuyuki MIURA, "Convex Grid Drawings of Plane Graphs with Pentagonal Contours on O(n2) Grids" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 9, pp. 1142-1149, September 2021, doi: 10.1587/transfun.2020DMP0011.
Abstract: In a convex grid drawing of a plane graph, all edges are drawn as straight-line segments without any edge-intersection, all vertices are put on grid points and all facial cycles are drawn as convex polygons. 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-1)×(n-1) grid if either 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. An internally triconnected plane graph G has a convex grid drawing on a 2n×2n grid if T(G) has exactly four leaves. Furthermore, an internally triconnected plane graph G has a convex grid drawing on a 6n×n2 grid if T(G) has exactly five leaves. In this paper, we show that an internally triconnected plane graph G has a convex grid drawing on a 20n×16n grid if T(G) has exactly five leaves. We also present an algorithm to find such a drawing in linear time. This is the first algorithm that finds a convex grid drawing of such a plane graph G in a grid of O(n2) size.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020DMP0011/_p
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@ARTICLE{e104-a_9_1142,
author={Kei SATO, Kazuyuki MIURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Convex Grid Drawings of Plane Graphs with Pentagonal Contours on O(n2) Grids},
year={2021},
volume={E104-A},
number={9},
pages={1142-1149},
abstract={In a convex grid drawing of a plane graph, all edges are drawn as straight-line segments without any edge-intersection, all vertices are put on grid points and all facial cycles are drawn as convex polygons. 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-1)×(n-1) grid if either 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. An internally triconnected plane graph G has a convex grid drawing on a 2n×2n grid if T(G) has exactly four leaves. Furthermore, an internally triconnected plane graph G has a convex grid drawing on a 6n×n2 grid if T(G) has exactly five leaves. In this paper, we show that an internally triconnected plane graph G has a convex grid drawing on a 20n×16n grid if T(G) has exactly five leaves. We also present an algorithm to find such a drawing in linear time. This is the first algorithm that finds a convex grid drawing of such a plane graph G in a grid of O(n2) size.},
keywords={},
doi={10.1587/transfun.2020DMP0011},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - Convex Grid Drawings of Plane Graphs with Pentagonal Contours on O(n2) Grids
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1142
EP - 1149
AU - Kei SATO
AU - Kazuyuki MIURA
PY - 2021
DO - 10.1587/transfun.2020DMP0011
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2021
AB - In a convex grid drawing of a plane graph, all edges are drawn as straight-line segments without any edge-intersection, all vertices are put on grid points and all facial cycles are drawn as convex polygons. 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-1)×(n-1) grid if either 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. An internally triconnected plane graph G has a convex grid drawing on a 2n×2n grid if T(G) has exactly four leaves. Furthermore, an internally triconnected plane graph G has a convex grid drawing on a 6n×n2 grid if T(G) has exactly five leaves. In this paper, we show that an internally triconnected plane graph G has a convex grid drawing on a 20n×16n grid if T(G) has exactly five leaves. We also present an algorithm to find such a drawing in linear time. This is the first algorithm that finds a convex grid drawing of such a plane graph G in a grid of O(n2) size.
ER -
English
