Reconfiguration of list L(2, 1)-labelings in a graph

Takehiro Ito, Kazuto Kawamura, Hirotaka Ono, Xiao Zhou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationAlgorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings
PublisherSpringer Verlag
Number of pages10
ISBN (Print)9783642352607
Publication statusPublished - 2012
Event23rd International Symposium on Algorithms and Computation, ISAAC 2012 - Taipei, Taiwan, Province of China
Duration: Dec 19 2012Dec 21 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7676 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other23rd International Symposium on Algorithms and Computation, ISAAC 2012
Country/TerritoryTaiwan, Province of China

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)


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