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

8 years 22 days ago

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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

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