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

Takehiro Ito, Kazuto Kawamura, Hirotaka Ono, Xiao Zhou

研究成果: Conference contribution

8 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルAlgorithms and Computation - 23rd International Symposium, ISAAC 2012, Proceedings
出版社Springer Verlag
ページ34-43
ページ数10
ISBN(印刷版)9783642352607
DOI
出版ステータスPublished - 2012
イベント23rd International Symposium on Algorithms and Computation, ISAAC 2012 - Taipei, Taiwan, Province of China
継続期間: 2012 12 192012 12 21

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
7676 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

Other

Other23rd International Symposium on Algorithms and Computation, ISAAC 2012
国/地域Taiwan, Province of China
CityTaipei
Period12/12/1912/12/21

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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