## 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 seriesparallel 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.

Original language | English |
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Pages (from-to) | 1168-1178 |

Number of pages | 11 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E98A |

Issue number | 6 |

DOIs | |

Publication status | Published - 2015 Jun 1 |

Externally published | Yes |

## Keywords

- Graph algorithm
- List coloring
- PSPACE-complete
- Pathwidth
- Reachability on solution space
- Reconfiguration

## ASJC Scopus subject areas

- Signal Processing
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering
- Applied Mathematics