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

8 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
Title of host publicationAlgorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings
Pages34-43
Number of pages10
Publication statusPublished - Dec 31 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

Other

Other23rd International Symposium on Algorithms and Computation, ISAAC 2012
CountryTaiwan, Province of China
CityTaipei
Period12/19/1212/21/12

Fingerprint

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

Ito, T., Kawamura, K., Ono, H., & Zhou, X. (2012). Reconfiguration of list L(2, 1)-labelings in a graph. In Algorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings (pp. 34-43). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7676 LNCS).

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

Algorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings. 2012. p. 34-43 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7676 LNCS).

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

Ito, T, Kawamura, K, Ono, H & Zhou, X 2012, Reconfiguration of list L(2, 1)-labelings in a graph. in Algorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7676 LNCS, pp. 34-43, 23rd International Symposium on Algorithms and Computation, ISAAC 2012, Taipei, Taiwan, Province of China, 12/19/12.
Ito T, Kawamura K, Ono H, Zhou X. Reconfiguration of list L(2, 1)-labelings in a graph. In Algorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings. 2012. p. 34-43. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Ito, Takehiro ; Kawamura, Kazuto ; Ono, Hirotaka ; Zhou, Xiao. / Reconfiguration of list L(2, 1)-labelings in a graph. Algorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings. 2012. pp. 34-43 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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