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On the Lucky Choice Number of Graphs

Akbari, S ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1007/s00373-011-1112-4
  3. Publisher: 2013
  4. Abstract:
  5. Suppose that G is a graph and f: V (G) → ℕ is a labeling of the vertices of G. Let S(v) denote the sum of labels over all neighbors of the vertex v in G. A labeling f of G is called lucky if S(u) ≠ S(v) for every pair of adjacent vertices u and v. Also, for each vertex v ∈ V(G), let L(v) denote a list of natural numbers available at v. A list lucky labeling, is a lucky labeling f such that f(v) ∈ L(v) for each v ∈ V(G). A graph G is said to be lucky k-choosable if every k-list assignment of natural numbers to the vertices of G permits a list lucky labeling of G. The lucky choice number of G, ηl(G), is the minimum natural number k such that G is lucky k-choosable. In this paper, we prove that for every graph G with Δ ≥ 2, η(G) ≤ Δ2 - <Δ + 1, where Δ denotes the maximum degree of G. Among other results we show that for every 3-list assignment to the vertices of a forest, there is a list lucky labeling which is a proper vertex coloring too
  6. Keywords:
  7. Combinatorial Nullstellensatz ; Lucky choice number ; Lucky choosable ; Lucky labeling
  8. Source: Graphs and Combinatorics ; Volume 29, Issue 2 , 2013 , Pages 157-163 ; 09110119 (ISSN)
  9. URL: http://link.springer.com/article/10.1007%2Fs00373-011-1112-4