IEICE TRANSACTIONS on Fundamentals
A Note on the Intersection of Alternately Orientable Graphs and Cocomparability Graphs
Summary :
We studied whether a statement similar to the Ghouila-Houri's theorem might hold for alternating orientations of cocomparability graphs. In this paper, we give the negative answer. We prove that it is NP-complete to decide whether a cocomparability graph has an orientation that is alternating and acyclic. Hence, cocomparability graphs with an acyclic alternating orientation form a proper subclass of alternately orientable cocomparability graphs. We also provide a separating example, that is, an alternately orientable cocomparability graph such that no alternating orientation is acyclic.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.9 pp.1223-1227
- Publication Date
- 2022/09/01
- Publicized
- 2022/03/07
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.2021DMP0001
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
- Graphs and Networks, Algorithms and Data Structures
Authors
Asahi TAKAOKA
Muroran Institute of Technology
Keyword
Latest Issue
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Asahi TAKAOKA, "A Note on the Intersection of Alternately Orientable Graphs and Cocomparability Graphs" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 9, pp. 1223-1227, September 2022, doi: 10.1587/transfun.2021DMP0001.
Abstract: We studied whether a statement similar to the Ghouila-Houri's theorem might hold for alternating orientations of cocomparability graphs. In this paper, we give the negative answer. We prove that it is NP-complete to decide whether a cocomparability graph has an orientation that is alternating and acyclic. Hence, cocomparability graphs with an acyclic alternating orientation form a proper subclass of alternately orientable cocomparability graphs. We also provide a separating example, that is, an alternately orientable cocomparability graph such that no alternating orientation is acyclic.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021DMP0001/_p
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@ARTICLE{e105-a_9_1223,
author={Asahi TAKAOKA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Note on the Intersection of Alternately Orientable Graphs and Cocomparability Graphs},
year={2022},
volume={E105-A},
number={9},
pages={1223-1227},
abstract={We studied whether a statement similar to the Ghouila-Houri's theorem might hold for alternating orientations of cocomparability graphs. In this paper, we give the negative answer. We prove that it is NP-complete to decide whether a cocomparability graph has an orientation that is alternating and acyclic. Hence, cocomparability graphs with an acyclic alternating orientation form a proper subclass of alternately orientable cocomparability graphs. We also provide a separating example, that is, an alternately orientable cocomparability graph such that no alternating orientation is acyclic.},
keywords={},
doi={10.1587/transfun.2021DMP0001},
ISSN={1745-1337},
month={September},}
Copy
TY - JOUR
TI - A Note on the Intersection of Alternately Orientable Graphs and Cocomparability Graphs
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1223
EP - 1227
AU - Asahi TAKAOKA
PY - 2022
DO - 10.1587/transfun.2021DMP0001
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E105-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2022
AB - We studied whether a statement similar to the Ghouila-Houri's theorem might hold for alternating orientations of cocomparability graphs. In this paper, we give the negative answer. We prove that it is NP-complete to decide whether a cocomparability graph has an orientation that is alternating and acyclic. Hence, cocomparability graphs with an acyclic alternating orientation form a proper subclass of alternately orientable cocomparability graphs. We also provide a separating example, that is, an alternately orientable cocomparability graph such that no alternating orientation is acyclic.
ER -
English
