Geodesic
Performance ratio of the generalized greedy algorithm for $q$-coloring problem
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2007), pp. 53-58.

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In this paper a generalized greedy algorithm finding $q$-colorable subgraph is described, where $q$ is a natural number, and it is proven that the performance ratio of the described algorithm does not exceed $\dfrac{e}{e-1}$ for arbitrary $q$. Then it is shown that the performance ratio of the simple greedy algorithm also doesn't exceed $\dfrac{e}{e-1}$. Thus, it follows that the performance ratio $2$ previously found for simple greedy algorithm is not attainable. 
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R. O. Adamyan. Performance ratio of the generalized greedy algorithm for $q$-coloring problem. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 2 (2007), pp. 53-58. http://geodesic.mathdoc.fr/item/UZERU_2007_2_a6/

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