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2016

First-fit coloring on interval graphs has performance ratio at least 5

3 years 19 days ago
First-fit coloring on interval graphs has performance ratio at least 5
First-fit is the online graph coloring algorithm that considers vertices one at a time in some order and assigns each vertex the least positive integer not used already on a neighbor. The maximum number of colors used by first-fit on graph G over all vertex orders is denoted χF F (G). The exact value of R := supG χF F (G) ω(G) over interval graphs G is unknown. Pemmaraju, Raman, and Varadarajan proved R ≤ 10, and this can be improved to 8. Witsenhausen and Chrobak and ´Slusarek showed R ≥ 4, and ´Slusarek improved this to 4.45. We prove R ≥ 5. Key words: graph coloring, online algorithm, first-fit, interval graph.
Hal A. Kierstead, David A. Smith, William T. Trott
Added 02 Apr 2016
Updated 02 Apr 2016
Type Journal
Year 2016
Where EJC
Authors Hal A. Kierstead, David A. Smith, William T. Trotter
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