On-line rankings of graphs

I. Schiermeyer, Z. Tuza, M. Voigt

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

A (vertex) k-ranking of a graph G = (V, E) is a proper vertex coloring φ : V → {1,...,k} such that each path with endvertices of the same color i contains an internal vertex of color ≥ i + 1. In the on-line coloring algorithms, the vertices v1,...,vn arrive one by one in an unrestricted order, and only the edges inside the set {v1,...,vi} are known when the color of vi has to be chosen. We characterize those graphs for which a 3-ranking can be found on-line. We also prove that the greedy (First-Fit) on-line algorithm, assigning the smallest feasible color to the next vertex at each step, generates a (3 log2 n)-ranking for the path with n ≥ 2 vertices, independently of the order in which the vertices are received.

Original languageEnglish
Pages (from-to)141-147
Number of pages7
JournalDiscrete Mathematics
Volume212
Issue number1-2
Publication statusPublished - Feb 6 2000

Fingerprint

Ranking
Color
Coloring
Graph in graph theory
Vertex of a graph
Path
Vertex Coloring
Colouring
Internal

Keywords

  • On-line coloring algorithm
  • Vertex coloring
  • Vertex ranking

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Theoretical Computer Science

Cite this

Schiermeyer, I., Tuza, Z., & Voigt, M. (2000). On-line rankings of graphs. Discrete Mathematics, 212(1-2), 141-147.

On-line rankings of graphs. / Schiermeyer, I.; Tuza, Z.; Voigt, M.

In: Discrete Mathematics, Vol. 212, No. 1-2, 06.02.2000, p. 141-147.

Research output: Contribution to journalArticle

Schiermeyer, I, Tuza, Z & Voigt, M 2000, 'On-line rankings of graphs', Discrete Mathematics, vol. 212, no. 1-2, pp. 141-147.
Schiermeyer I, Tuza Z, Voigt M. On-line rankings of graphs. Discrete Mathematics. 2000 Feb 6;212(1-2):141-147.
Schiermeyer, I. ; Tuza, Z. ; Voigt, M. / On-line rankings of graphs. In: Discrete Mathematics. 2000 ; Vol. 212, No. 1-2. pp. 141-147.
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