List version of L (d,s)-labelings

Anja Kohl, Jens Schreyer, Z. Tuza, Margit Voigt

Research output: Article

3 Citations (Scopus)

Abstract

Let G=(V,E) be a simple graph, and for all v∈V, let L(v) be a list of colors assigned to v. We shall assume throughout that the colors are natural numbers. For nonnegative integers d,s, define χℓd,s(G) to be the smallest integer k such that for every list assignment with |L(v)|=k for all v∈V one can choose a color c(v)∈L(v) for every vertex in such a way that |c(v)-c(w)|≥d for all vw∈E and |c(v)-c(w)|≥s for all pairs v,w of vertices having distance 2 in G. For a given list assignment such a coloring c is called an L(d,s)-list labeling. We prove a general bound for χℓd,s(G) depending on the maximum degree of G. Furthermore, we study this parameter for trees, and also for the particular classes of paths and stars. Polynomial algorithms are designed for deciding whether a given list assignment admits an L(d,s)-list labeling on paths (for a given s unrestricted) and on trees (for s=1).

Original languageEnglish
Pages (from-to)92-98
Number of pages7
JournalTheoretical Computer Science
Volume349
Issue number1
DOIs
Publication statusPublished - dec. 12 2005

Fingerprint

Labeling
Assignment
Color
Path
Integer
Polynomial Algorithm
Coloring
Simple Graph
Maximum Degree
Natural number
Stars
Colouring
Star
Choose
Non-negative
Polynomials
Vertex of a graph
Class

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

List version of L (d,s)-labelings. / Kohl, Anja; Schreyer, Jens; Tuza, Z.; Voigt, Margit.

In: Theoretical Computer Science, Vol. 349, No. 1, 12.12.2005, p. 92-98.

Research output: Article

Kohl, Anja ; Schreyer, Jens ; Tuza, Z. ; Voigt, Margit. / List version of L (d,s)-labelings. In: Theoretical Computer Science. 2005 ; Vol. 349, No. 1. pp. 92-98.
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