On-line rankings of graphs

I. Schiermeyer, Zs 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
DOIs
Publication statusPublished - Feb 6 2000

Keywords

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

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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