Let A be a graph coloring algorithm. Denote by <italic>-&-Agrave; (G)</italic> the ratio between the maximum number of colors A will use to color the graph <italic>G,</italic> and the chromatic number of <italic>G,</italic><subscrpt>x</subscrpt><italic>(G)</italic>. For most existing <bold>polynomial</bold> coloring algorithms, <italic>-&-Agrave;(G)</italic> can be as bad as O<italic>(n),</italic> where <italic>n</italic> is the number of vertices in <italic>G</italic>. The best currently known algorithm guarantees <italic>-&-Agrave; (G)-&-equil;O(n/</italic>log<italic>n</italic>). In this paper we present a simple and efficient coloring algorithm which guarantees <italic>-&-Agrave;(G)-&-le;x(G)n</italic> (equation), a considerable improvem-&-edot;nt over the current bounds.
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