IEICE TRANSACTIONS on Fundamentals
On the Structure of Locally Outerplanar Graphs
Summary :
For k ≥ 3, a convex geometric graph is called k-locally outerplanar if no path of length k intersects itself. In [D. Boutin, Convex Geometric Graphs with No Short Self-intersecting Path, Congressus Numerantium 160 (2003) 205-214], Boutin stated the results of the degeneracy for 3-locally outerplanar graphs. Later, in [D. Boutin, Structure and Properties of Locally Outerplanar Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 60 (2007) 169-180], a structural property on k-locally outerplanar graphs was proposed. These results are based on the existence of “minimal corner pairs”. In this paper, we show that a “minimal corner pair” may not exist and give a counterexample to disprove the structural property. Furthermore, we generalize the result on the degeneracy with respect to k-locally outerplanar graphs.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.6 pp.1212-1215
- Publication Date
- 2015/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E98.A.1212
- Type of Manuscript
- Special Section LETTER (Special Section on Discrete Mathematics and Its Applications)
- Category
Authors
Hung-Lung WANG
National Taipei University of Business
Chun-Yu TSENG
National Taipei University of Business
Jou-Ming CHANG
National Taipei University of Business
Keyword
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Hung-Lung WANG, Chun-Yu TSENG, Jou-Ming CHANG, "On the Structure of Locally Outerplanar Graphs" in IEICE TRANSACTIONS on Fundamentals,
vol. E98-A, no. 6, pp. 1212-1215, June 2015, doi: 10.1587/transfun.E98.A.1212.
Abstract: For k ≥ 3, a convex geometric graph is called k-locally outerplanar if no path of length k intersects itself. In [D. Boutin, Convex Geometric Graphs with No Short Self-intersecting Path, Congressus Numerantium 160 (2003) 205-214], Boutin stated the results of the degeneracy for 3-locally outerplanar graphs. Later, in [D. Boutin, Structure and Properties of Locally Outerplanar Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 60 (2007) 169-180], a structural property on k-locally outerplanar graphs was proposed. These results are based on the existence of “minimal corner pairs”. In this paper, we show that a “minimal corner pair” may not exist and give a counterexample to disprove the structural property. Furthermore, we generalize the result on the degeneracy with respect to k-locally outerplanar graphs.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.1212/_p
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@ARTICLE{e98-a_6_1212,
author={Hung-Lung WANG, Chun-Yu TSENG, Jou-Ming CHANG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the Structure of Locally Outerplanar Graphs},
year={2015},
volume={E98-A},
number={6},
pages={1212-1215},
abstract={For k ≥ 3, a convex geometric graph is called k-locally outerplanar if no path of length k intersects itself. In [D. Boutin, Convex Geometric Graphs with No Short Self-intersecting Path, Congressus Numerantium 160 (2003) 205-214], Boutin stated the results of the degeneracy for 3-locally outerplanar graphs. Later, in [D. Boutin, Structure and Properties of Locally Outerplanar Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 60 (2007) 169-180], a structural property on k-locally outerplanar graphs was proposed. These results are based on the existence of “minimal corner pairs”. In this paper, we show that a “minimal corner pair” may not exist and give a counterexample to disprove the structural property. Furthermore, we generalize the result on the degeneracy with respect to k-locally outerplanar graphs.},
keywords={},
doi={10.1587/transfun.E98.A.1212},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - On the Structure of Locally Outerplanar Graphs
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1212
EP - 1215
AU - Hung-Lung WANG
AU - Chun-Yu TSENG
AU - Jou-Ming CHANG
PY - 2015
DO - 10.1587/transfun.E98.A.1212
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2015
AB - For k ≥ 3, a convex geometric graph is called k-locally outerplanar if no path of length k intersects itself. In [D. Boutin, Convex Geometric Graphs with No Short Self-intersecting Path, Congressus Numerantium 160 (2003) 205-214], Boutin stated the results of the degeneracy for 3-locally outerplanar graphs. Later, in [D. Boutin, Structure and Properties of Locally Outerplanar Graphs, Journal of Combinatorial Mathematics and Combinatorial Computing 60 (2007) 169-180], a structural property on k-locally outerplanar graphs was proposed. These results are based on the existence of “minimal corner pairs”. In this paper, we show that a “minimal corner pair” may not exist and give a counterexample to disprove the structural property. Furthermore, we generalize the result on the degeneracy with respect to k-locally outerplanar graphs.
ER -
English
