On the first-fit chromatic number of graphs

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

doi:10.1137/060672479

On the first-fit chromatic number of graphs

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

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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,..., V_k so that for each 1 ≤ i < j ≤ k and for each x ∈ V_j there exists a y ∈ V_i 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 language	English (US)
Pages (from-to)	887-900
Number of pages	14
Journal	SIAM Journal on Discrete Mathematics
Volume	22
Issue number	3
DOIs	https://doi.org/10.1137/060672479
State	Published - Dec 1 2008

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

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10.1137/060672479

Cite this

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abstract = "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.",

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On the first-fit chromatic number of graphs

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Keywords

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