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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

Asahi TAKAOKA

Muroran Institute of Technology

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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},}

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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 -