On the first-fit chromatic number of graphs

József Balogh, Stephen G. Hartke, Qi Liu, Gexin Yu

Research output: Contribution to journalArticlepeer-review


The first-fit chromatic number of a graph is the number of colors needed in the worst case of a greedy coloring. It is also called the Grundy number, which is defined to be the maximum number of classes in an ordered partition of the vertex set of a graph G into independent sets V1, V2,..., Vk so that for each 1 ≤ i < j ≤ k and for each x ∈ Vj there exists a y ∈ Vi such that x and y are adjacent. In this paper, we study the first-fit chromatic number of outerplanar and planar graphs as well as Cartesian products of graphs, and in particular we give asymptotically tight results for outerplanar graphs.

Original languageEnglish (US)
Pages (from-to)887-900
Number of pages14
JournalSIAM Journal on Discrete Mathematics
Issue number3
StatePublished - Dec 1 2008


  • Cartesian product
  • First-fit chromatic number
  • Greedy coloring
  • Grundy coloring
  • Grundy number
  • Planar graph
  • Random graph

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'On the first-fit chromatic number of graphs'. Together they form a unique fingerprint.

Cite this