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

Takehiro Ito, Kazuto Kawamura, Hirotaka Ono, Xiao Zhou

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

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
Pages (from-to)84-97
Number of pages14
JournalTheoretical Computer Science
Volume544
Issue numberC
DOIs
Publication statusPublished - Jan 1 2014

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L(2, 1)-labeling
Reconfiguration
Labeling
Labels
Graph in graph theory
Assignment
Vertex of a graph
Decision problem
Bipartite Graph
Planar graph
Linear Time
Adjacent
Integer
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Reconfiguration of list L(2, 1)-labelings in a graph. / Ito, Takehiro; Kawamura, Kazuto; Ono, Hirotaka; Zhou, Xiao.

In: Theoretical Computer Science, Vol. 544, No. C, 01.01.2014, p. 84-97.

Research output: Contribution to journalArticle

Ito, Takehiro ; Kawamura, Kazuto ; Ono, Hirotaka ; Zhou, Xiao. / Reconfiguration of list L(2, 1)-labelings in a graph. In: Theoretical Computer Science. 2014 ; Vol. 544, No. C. pp. 84-97.
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