For an integer k ≥ 0, suppose that each vertex v of a graph G has a set C(v) ⊆ {0, 1, . . . , k} of labels, called a list of v. A list L(2, 1)-labeling of G is an assignment of a label in C(v) to each vertex v of G such that every two adjacent vertices receive labels which differ by at least 2 and every two vertices of distance two receive labels which differ by at least 1. In this paper, we study the problem of reconfiguring one list L(2, 1)-labeling of a graph into another list L(2, 1)-labeling of the same graph by changing only one label assignment at a time, while at all times maintaining a list L(2, 1)-labeling. First we show that this decision problem is PSPACE-complete, even for bipartite planar graphs and k ≥ 6. In contrast, we then show that the problem can be solved in linear time for general graphs if k ≤ 4. We finally consider the problem restricted to trees, and give a sufficient condition for which any two list L(2, 1)-labelings of a tree can be transformed into each other. © Springer-Verlag 2012.
CITATION STYLE
Ito, T., Kawamura, K., Ono, H., & Zhou, X. (2012). Reconfiguration of list L(2, 1)-labelings in a graph. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7676 LNCS, pp. 34–43). Springer Verlag. https://doi.org/10.1007/978-3-642-35261-4_7
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