### 抜粋

An L(2,1)-labeling of a graph G is an assignment f from the vertex set V(G) to the set of nonnegative integers such that |f(x)-f(y)|≥2 if x and y are adjacent and |f(x)-f(y)|≥1 if x and y are at distance 2, for all x and y in V(G). A k-L(2,1)-labeling is an L(2,1)-labeling f:V(G)→{0,...,k}, and the L(2,1)-labeling problem asks the minimum k, which we denote by λ(G), among all possible assignments. It is known that this problem is NP-hard even for graphs of treewidth 2, and tree is one of very few classes for which the problem is polynomially solvable. The running time of the best known algorithm for trees had been O(Δ^{4.5} n) for more than a decade, and an O( min {n ^{1.75},Δ^{1.5} n})-time algorithm has appeared recently, where Δ is the maximum degree of T and n=|V(T)|, however, it has been open if it is solvable in linear time. In this paper, we finally settle this problem for L(2,1)-labeling of trees by establishing a linear time algorithm.

元の言語 | 英語 |
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ホスト出版物のタイトル | Algorithms - ESA 2009 - 17th Annual European Symposium, Proceedings |

ページ | 35-46 |

ページ数 | 12 |

DOI | |

出版物ステータス | 出版済み - 11 2 2009 |

イベント | 17th Annual European Symposium on Algorithms, ESA 2009 - Copenhagen, デンマーク 継続期間: 9 7 2009 → 9 9 2009 |

### 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) |
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巻 | 5757 LNCS |

ISSN（印刷物） | 0302-9743 |

ISSN（電子版） | 1611-3349 |

### その他

その他 | 17th Annual European Symposium on Algorithms, ESA 2009 |
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国 | デンマーク |

市 | Copenhagen |

期間 | 9/7/09 → 9/9/09 |

### フィンガープリント

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### これを引用

*Algorithms - ESA 2009 - 17th Annual European Symposium, Proceedings*(pp. 35-46). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 5757 LNCS). https://doi.org/10.1007/978-3-642-04128-0_4