IEICE TRANSACTIONS on Fundamentals
Convex Grid Drawings of Internally Triconnected Plane Graphs with Pentagonal Contours
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 20n × 16n 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 10n × 5n grid if T(G) has exactly five leaves. We also present a linear-time algorithm to find such a drawing.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E106-A No.9 pp.1092-1099
- Publication Date
- 2023/09/01
- Publicized
- 2023/03/06
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2022DMP0009
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
- Algorithms and Data Structures
Authors
Kazuyuki MIURA
Fukushima University
Keyword
Latest Issue
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Kazuyuki MIURA, "Convex Grid Drawings of Internally Triconnected Plane Graphs with Pentagonal Contours" in IEICE TRANSACTIONS on Fundamentals,
vol. E106-A, no. 9, pp. 1092-1099, September 2023, doi: 10.1587/transfun.2022DMP0009.
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 20n × 16n 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 10n × 5n grid if T(G) has exactly five leaves. We also present a linear-time algorithm to find such a drawing.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2022DMP0009/_p
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@ARTICLE{e106-a_9_1092,
author={Kazuyuki MIURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Convex Grid Drawings of Internally Triconnected Plane Graphs with Pentagonal Contours},
year={2023},
volume={E106-A},
number={9},
pages={1092-1099},
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 20n × 16n 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 10n × 5n grid if T(G) has exactly five leaves. We also present a linear-time algorithm to find such a drawing.},
keywords={},
doi={10.1587/transfun.2022DMP0009},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - Convex Grid Drawings of Internally Triconnected Plane Graphs with Pentagonal Contours
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1092
EP - 1099
AU - Kazuyuki MIURA
PY - 2023
DO - 10.1587/transfun.2022DMP0009
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E106-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2023
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 20n × 16n 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 10n × 5n grid if T(G) has exactly five leaves. We also present a linear-time algorithm to find such a drawing.
ER -
English
