The (p,q)-total labeling problem for trees

Toru Hasunuma, Toshimasa Ishii, Hirotaka Ono, Yushi Uno

研究成果: 著書/レポートタイプへの貢献会議での発言

抜粋

A (p,q)-total labeling of a graph G is an assignment f from the vertex set V(G) and the edge set E(G) to the set of nonnegative integers such that |f(x)-f(y)| ≥ p if x is a vertex and y is an edge incident to x, and |f(x) - f(y)| ≥ q if x and y are a pair of adjacent vertices or a pair of adjacent edges, for all x and y in V(G) ∪ E(G). A k-(p,q)-total labeling is a (p,q)-total labeling f:V(G) ∪ E(G)→{0,...,k}, and the (p,q)-total labeling problem asks the minimum k, which we denote by λ pqT(G), among all possible assignments. In this paper, we first give new upper and lower bounds on λpqT(G) for some classes of graphs G, in particular, tight bounds on λpqT(T) for trees T. We then show that if p ≤ 3q/2, the problem for trees T is linearly solvable, and give a complete characterization of trees achieving λpqT(T) if in addition Δ ≥ 4 holds, where Δ is the maximum degree of T. It is contrasting to the fact that the L(p,q)-labeling problem, which is a generalization of the (p,q)-total labeling problem, is NP-hard for any two positive integers p and q such that q is not a divisor of p.

元の言語英語
ホスト出版物のタイトルAlgorithms and Computation - 21st International Symposium, ISAAC 2010, Proceedings
ページ49-60
ページ数12
エディションPART 2
DOI
出版物ステータス出版済み - 12 1 2010
イベント21st Annual International Symposium on Algorithms and Computations, ISAAC 2010 - Jeju Island, 大韓民国
継続期間: 12 15 201012 17 2010

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)
番号PART 2
6507 LNCS
ISSN(印刷物)0302-9743
ISSN(電子版)1611-3349

その他

その他21st Annual International Symposium on Algorithms and Computations, ISAAC 2010
大韓民国
Jeju Island
期間12/15/1012/17/10

    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

Hasunuma, T., Ishii, T., Ono, H., & Uno, Y. (2010). The (p,q)-total labeling problem for trees. : Algorithms and Computation - 21st International Symposium, ISAAC 2010, Proceedings (PART 2 版, pp. 49-60). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); 巻数 6507 LNCS, 番号 PART 2). https://doi.org/10.1007/978-3-642-17514-5_5