IEICE TRANSACTIONS on Fundamentals
The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs
Summary :
We study the problem of transforming one list (vertex) coloring of a graph into another list coloring by changing only one vertex color assignment at a time, while at all times maintaining a list coloring, given a list of allowed colors for each vertex. This problem is known to be PSPACE-complete for bipartite planar graphs. In this paper, we first show that the problem remains PSPACE-complete even for bipartite series-parallel graphs, which form a proper subclass of bipartite planar graphs. We note that our reduction indeed shows the PSPACE-completeness for graphs with pathwidth two, and it can be extended for threshold graphs. In contrast, we give a polynomial-time algorithm to solve the problem for graphs with pathwidth one. Thus, this paper gives sharp analyses of the problem with respect to pathwidth.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.6 pp.1168-1178
- Publication Date
- 2015/06/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E98.A.1168
- Type of Manuscript
- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
- Category
Authors
Tatsuhiko HATANAKA
Tohoku University
Takehiro ITO
Tohoku University
Xiao ZHOU
Tohoku University
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
Tatsuhiko HATANAKA, Takehiro ITO, Xiao ZHOU, "The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs" in IEICE TRANSACTIONS on Fundamentals,
vol. E98-A, no. 6, pp. 1168-1178, June 2015, doi: 10.1587/transfun.E98.A.1168.
Abstract: We study the problem of transforming one list (vertex) coloring of a graph into another list coloring by changing only one vertex color assignment at a time, while at all times maintaining a list coloring, given a list of allowed colors for each vertex. This problem is known to be PSPACE-complete for bipartite planar graphs. In this paper, we first show that the problem remains PSPACE-complete even for bipartite series-parallel graphs, which form a proper subclass of bipartite planar graphs. We note that our reduction indeed shows the PSPACE-completeness for graphs with pathwidth two, and it can be extended for threshold graphs. In contrast, we give a polynomial-time algorithm to solve the problem for graphs with pathwidth one. Thus, this paper gives sharp analyses of the problem with respect to pathwidth.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.1168/_p
Copy
@ARTICLE{e98-a_6_1168,
author={Tatsuhiko HATANAKA, Takehiro ITO, Xiao ZHOU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs},
year={2015},
volume={E98-A},
number={6},
pages={1168-1178},
abstract={We study the problem of transforming one list (vertex) coloring of a graph into another list coloring by changing only one vertex color assignment at a time, while at all times maintaining a list coloring, given a list of allowed colors for each vertex. This problem is known to be PSPACE-complete for bipartite planar graphs. In this paper, we first show that the problem remains PSPACE-complete even for bipartite series-parallel graphs, which form a proper subclass of bipartite planar graphs. We note that our reduction indeed shows the PSPACE-completeness for graphs with pathwidth two, and it can be extended for threshold graphs. In contrast, we give a polynomial-time algorithm to solve the problem for graphs with pathwidth one. Thus, this paper gives sharp analyses of the problem with respect to pathwidth.},
keywords={},
doi={10.1587/transfun.E98.A.1168},
ISSN={1745-1337},
month={June},}
Copy
TY - JOUR
TI - The List Coloring Reconfiguration Problem for Bounded Pathwidth Graphs
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1168
EP - 1178
AU - Tatsuhiko HATANAKA
AU - Takehiro ITO
AU - Xiao ZHOU
PY - 2015
DO - 10.1587/transfun.E98.A.1168
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 6
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - June 2015
AB - We study the problem of transforming one list (vertex) coloring of a graph into another list coloring by changing only one vertex color assignment at a time, while at all times maintaining a list coloring, given a list of allowed colors for each vertex. This problem is known to be PSPACE-complete for bipartite planar graphs. In this paper, we first show that the problem remains PSPACE-complete even for bipartite series-parallel graphs, which form a proper subclass of bipartite planar graphs. We note that our reduction indeed shows the PSPACE-completeness for graphs with pathwidth two, and it can be extended for threshold graphs. In contrast, we give a polynomial-time algorithm to solve the problem for graphs with pathwidth one. Thus, this paper gives sharp analyses of the problem with respect to pathwidth.
ER -
English
