IEICE TRANSACTIONS on Information
The Coloring Reconfiguration Problem on Specific Graph Classes
Summary :
We study the problem of transforming one (vertex) c-coloring of a graph into another one by changing only one vertex color assignment at a time, while at all times maintaining a c-coloring, where c denotes the number of colors. This decision problem is known to be PSPACE-complete even for bipartite graphs and any fixed constant c ≥ 4. In this paper, we study the problem from the viewpoint of graph classes. We first show that the problem remains PSPACE-complete for chordal graphs even if c is a fixed constant. We then demonstrate that, even when c is a part of input, the problem is solvable in polynomial time for several graph classes, such as k-trees with any integer k ≥ 1, split graphs, and trivially perfect graphs.
- Publication
- IEICE TRANSACTIONS on Information Vol.E102-D No.3 pp.423-429
- Publication Date
- 2019/03/01
- Publicized
- 2018/10/30
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.2018FCP0005
- Type of Manuscript
- Special Section PAPER (Special Section on Foundations of Computer Science — Algorithm, Theory of Computation, and their Applications —)
- Category
Authors
Tatsuhiko HATANAKA
Tohoku University
Takehiro ITO
Tohoku University
Xiao ZHOU
Tohoku University
Keyword
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Tatsuhiko HATANAKA, Takehiro ITO, Xiao ZHOU, "The Coloring Reconfiguration Problem on Specific Graph Classes" in IEICE TRANSACTIONS on Information,
vol. E102-D, no. 3, pp. 423-429, March 2019, doi: 10.1587/transinf.2018FCP0005.
Abstract: We study the problem of transforming one (vertex) c-coloring of a graph into another one by changing only one vertex color assignment at a time, while at all times maintaining a c-coloring, where c denotes the number of colors. This decision problem is known to be PSPACE-complete even for bipartite graphs and any fixed constant c ≥ 4. In this paper, we study the problem from the viewpoint of graph classes. We first show that the problem remains PSPACE-complete for chordal graphs even if c is a fixed constant. We then demonstrate that, even when c is a part of input, the problem is solvable in polynomial time for several graph classes, such as k-trees with any integer k ≥ 1, split graphs, and trivially perfect graphs.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2018FCP0005/_p
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@ARTICLE{e102-d_3_423,
author={Tatsuhiko HATANAKA, Takehiro ITO, Xiao ZHOU, },
journal={IEICE TRANSACTIONS on Information},
title={The Coloring Reconfiguration Problem on Specific Graph Classes},
year={2019},
volume={E102-D},
number={3},
pages={423-429},
abstract={We study the problem of transforming one (vertex) c-coloring of a graph into another one by changing only one vertex color assignment at a time, while at all times maintaining a c-coloring, where c denotes the number of colors. This decision problem is known to be PSPACE-complete even for bipartite graphs and any fixed constant c ≥ 4. In this paper, we study the problem from the viewpoint of graph classes. We first show that the problem remains PSPACE-complete for chordal graphs even if c is a fixed constant. We then demonstrate that, even when c is a part of input, the problem is solvable in polynomial time for several graph classes, such as k-trees with any integer k ≥ 1, split graphs, and trivially perfect graphs.},
keywords={},
doi={10.1587/transinf.2018FCP0005},
ISSN={1745-1361},
month={March},}
Copy
TY - JOUR
TI - The Coloring Reconfiguration Problem on Specific Graph Classes
T2 - IEICE TRANSACTIONS on Information
SP - 423
EP - 429
AU - Tatsuhiko HATANAKA
AU - Takehiro ITO
AU - Xiao ZHOU
PY - 2019
DO - 10.1587/transinf.2018FCP0005
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E102-D
IS - 3
JA - IEICE TRANSACTIONS on Information
Y1 - March 2019
AB - We study the problem of transforming one (vertex) c-coloring of a graph into another one by changing only one vertex color assignment at a time, while at all times maintaining a c-coloring, where c denotes the number of colors. This decision problem is known to be PSPACE-complete even for bipartite graphs and any fixed constant c ≥ 4. In this paper, we study the problem from the viewpoint of graph classes. We first show that the problem remains PSPACE-complete for chordal graphs even if c is a fixed constant. We then demonstrate that, even when c is a part of input, the problem is solvable in polynomial time for several graph classes, such as k-trees with any integer k ≥ 1, split graphs, and trivially perfect graphs.
ER -
English
