On vertex rankings of graphs and its relatives

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4 Scopus citations

Abstract

Abstract A vertex ranking of a graph is an assignment of ranks (or colors) to the vertices of the graph, in such a way that any simple path connecting two vertices of equal rank, must contain a vertex of a higher rank. In this paper we study a relaxation of this notion, in which the requirement above should only hold for paths of some bounded length l for some fixed l. For instance, already the case l=2 exhibits quite a different behavior than proper coloring. We prove upper and lower bounds on the minimum number of ranks required for several graph families, such as trees, planar graphs, graphs excluding a fixed minor and degenerate graphs.

Original languageEnglish
Article number10102
Pages (from-to)1460-1467
Number of pages8
JournalDiscrete Mathematics
Volume338
Issue number8
DOIs
StatePublished - 6 Aug 2015

Keywords

  • Conflict-free coloring
  • Ordered coloring
  • Unique maximum coloring
  • Vertex ranking

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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