On‐line and first fit colorings of graphs

A. Gyárfás, J. Lehel

Research output: Contribution to journalArticle

132 Citations (Scopus)


A graph coloring algorithm that immediately colors the vertices taken from a list without looking ahead or changing colors already assigned is called “on‐line coloring.” The properties of on‐line colorings are investigated in several classes of graphs. In many cases we find on‐line colorings that use no more colors than some function of the largest clique size of the graph. We show that the first fit on‐line coloring has an absolute performance ratio of two for the complement of chordal graphs. We prove an upper bound for the performance ratio of the first fit coloring on interval graphs. It is also shown that there are simple families resisting any on‐line algorithm: no on‐line algorithm can color all trees by a bounded number of colors.

Original languageEnglish
Pages (from-to)217-227
Number of pages11
JournalJournal of Graph Theory
Issue number2
Publication statusPublished - 1988

ASJC Scopus subject areas

  • Geometry and Topology

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