Simple Combination of Algorithms for 4-colorable Graphs
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چکیده
In this paper, a combination of algorithms for graph coloring is discussed. The algorithms of KargerMotwani-Sudan and Blum-Karger can be combined in a simple way to yield a polynomial-time algorithm for an Õ(n7/18)-coloring of any n-vertex 4-colorable graph. This result can be generalized to k-colorable graphs to obtain a coloring with Õ(n 1− 1 (k+1)/3−4/(11k2−11k) ) colors, which slightly improves the bound given by Karger et al. of Õ(n1−3/(k+1)) colors, for any k ≥ 3.
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تاریخ انتشار 2002