TY - GEN

T1 - Algorithms for coloring reconfiguration under recolorability constraints

AU - Osawa, Hiroki

AU - Suzuki, Akira

AU - Ito, Takehiro

AU - Zhou, Xiao

N1 - Funding Information:
1 Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP17K12636 and JP18H04091, Japan. 2 Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP16K00004 and JP18H04091, Japan. 3 Partially supported by JSPS KAKENHI Grant Number JP16K00003, Japan.
Funding Information:
Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP17K12636 and JP18H04091, Japan. 2 Partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP16K00004 and JP18H04091, Japan. 3 Partially supported by JSPS KAKENHI Grant Number JP16K00003, Japan.
Publisher Copyright:
© Hiroki Osawa, Akira Suzuki, Takehiro Ito, and Xiao Zhou; licensed under Creative Commons License CC-BY

PY - 2018/12/1

Y1 - 2018/12/1

N2 - Coloring reconfiguration is one of the most well-studied reconfiguration problems. In the problem, we are given two (vertex-)colorings of a graph using at most k colors, and asked to determine whether there exists a transformation between them by recoloring only a single vertex at a time, while maintaining a k-coloring throughout. It is known that this problem is solvable in linear time for any graph if k ≤ 3, while is PSPACE-complete for a fixed k ≥ 4. In this paper, we further investigate the problem from the viewpoint of recolorability constraints, which forbid some pairs of colors to be recolored directly. More specifically, the recolorability constraint is given in terms of an undirected graph R such that each node in R corresponds to a color, and each edge in R represents a pair of colors that can be recolored directly. In this paper, we give a linear-time algorithm to solve the problem under such a recolorability constraint if R is of maximum degree at most two. In addition, we show that the minimum number of recoloring steps required for a desired transformation can be computed in linear time for a yes-instance. We note that our results generalize the known positive ones for coloring reconfiguration.

AB - Coloring reconfiguration is one of the most well-studied reconfiguration problems. In the problem, we are given two (vertex-)colorings of a graph using at most k colors, and asked to determine whether there exists a transformation between them by recoloring only a single vertex at a time, while maintaining a k-coloring throughout. It is known that this problem is solvable in linear time for any graph if k ≤ 3, while is PSPACE-complete for a fixed k ≥ 4. In this paper, we further investigate the problem from the viewpoint of recolorability constraints, which forbid some pairs of colors to be recolored directly. More specifically, the recolorability constraint is given in terms of an undirected graph R such that each node in R corresponds to a color, and each edge in R represents a pair of colors that can be recolored directly. In this paper, we give a linear-time algorithm to solve the problem under such a recolorability constraint if R is of maximum degree at most two. In addition, we show that the minimum number of recoloring steps required for a desired transformation can be computed in linear time for a yes-instance. We note that our results generalize the known positive ones for coloring reconfiguration.

KW - And phrases combinatorial reconfiguration

KW - Graph algorithm

KW - Graph coloring

UR - http://www.scopus.com/inward/record.url?scp=85063667636&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063667636&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ISAAC.2018.37

DO - 10.4230/LIPIcs.ISAAC.2018.37

M3 - Conference contribution

AN - SCOPUS:85063667636

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 37:1-37:13

BT - 29th International Symposium on Algorithms and Computation, ISAAC 2018

A2 - Hsu, Wen-Lian

A2 - Lee, Der-Tsai

A2 - Liao, Chung-Shou

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 29th International Symposium on Algorithms and Computation, ISAAC 2018

Y2 - 16 December 2018 through 19 December 2018

ER -