TY - GEN
T1 - Complexity of coloring reconfiguration under recolorability constraints
AU - Osawa, Hiroki
AU - Suzuki, Akira
AU - Ito, Takehiro
AU - Zhou, Xiao
N1 - Funding Information:
∗ This work is partially supported by JST CREST Grant Number JPMJCR1402, and JSPS KAKENHI Grant Numbers JP16K00003, JP16K00004 and JP17K12636, Japan.
PY - 2017/12/1
Y1 - 2017/12/1
N2 - For an integer k 1, k-coloring reconfiguration is one of the most well-studied reconfiguration problems, defined as follows: In the problem, we are given two (vertex)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper coloring. The problem is known to be PSPACE-complete if k 4, and solvable for any graph in polynomial time if k 3. In this paper, we introduce a recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. 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. We study the hardness of the problem based on the structure of recolorability constraints R. More specifically, we prove that the problem is PSPACE-complete if R is of maximum degree at least four, or has a connected component containing more than one cycle.
AB - For an integer k 1, k-coloring reconfiguration is one of the most well-studied reconfiguration problems, defined as follows: In the problem, we are given two (vertex)colorings of a graph using k colors, and asked to transform one into the other by recoloring only one vertex at a time, while at all times maintaining a proper coloring. The problem is known to be PSPACE-complete if k 4, and solvable for any graph in polynomial time if k 3. In this paper, we introduce a recolorability constraint on the k colors, which forbids some pairs of colors to be recolored directly. 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. We study the hardness of the problem based on the structure of recolorability constraints R. More specifically, we prove that the problem is PSPACE-complete if R is of maximum degree at least four, or has a connected component containing more than one cycle.
KW - Combinatorial reconfiguration
KW - Graph coloring
KW - Pspace-complete
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U2 - 10.4230/LIPIcs.ISAAC.2017.62
DO - 10.4230/LIPIcs.ISAAC.2017.62
M3 - Conference contribution
AN - SCOPUS:85038565407
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 28th International Symposium on Algorithms and Computation, ISAAC 2017
A2 - Tokuyama, Takeshi
A2 - Okamoto, Yoshio
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 28th International Symposium on Algorithms and Computation, ISAAC 2017
Y2 - 9 December 2017 through 22 December 2017
ER -