On the equality of the partial Grundy and upper ochromatic numbers of graphs

Paul Erdös, Stephen T. Hedetniemi, Renu C. Laskar, Geert C.E. Prins

Research output: Contribution to journalArticle

22 Citations (Scopus)


A (proper) k-coloring of a graph G is a partition Π = {V 1,V2,..., Vk} of V(G) into k independent sets, called color classes. In a k-coloring Π, a vertex v ∈ Vi is called a Grundy vertex if v is adjacent to at least one vertex in color class Vj, for every j, j < i. A k-coloring is called a Grundy coloring if every vertex is a Grundy vertex. A k-coloring is called a partial Grundy coloring if every color class contains at least one Grundy vertex. In this paper we introduce partial Grundy colorings, and relate them to parsimonious proper colorings introduced by Simmons in 1982.

Original languageEnglish
Pages (from-to)53-64
Number of pages12
JournalDiscrete Mathematics
Issue number1
Publication statusPublished - Oct 28 2003



  • Achromatic number
  • Chromatic number
  • Colorings
  • Grundy number

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Cite this