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A lower bound for approximating the Grundy number

Abstract : The grundy numbering of a graph is the maximum number of colors used by on-line first-fit coloring, under the worst order of arrival of vertices. The grundy numbering problem is to find this ordering. We prove that there is a constant c>1 so that approximating the grundy numbering problem within c is not possible, unless NP ⊆ RP
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Guy Kortsarz. A lower bound for approximating the Grundy number. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2007, 9 (1), pp.7--21. ⟨hal-00966515⟩

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