@article{oai:nagoya.repo.nii.ac.jp:00013168,
 author = {XIE, Xuzhen and ONO, Takao and HIRATA, Tomio},
 issue = {5},
 journal = {IEICE transactions on fundamentals of electronics, communications and computer sciences},
 month = {May},
 note = {Karger, Motwani and Sudan presented a graph coloring algorithm based on semidefinite programming, which colors any k-colorable graph with maximum degree Δ using Õ(Δ^1-2/k) colors. This algorithm leads to an algorithm for k-colorable graph using Õ(n ^1-3/^(k+1)) colors. This improved Wigderson's algorithm, which uses O(n^1-1/^(k-1)) colors, containing as a subroutine an algorithm using (Δ+1) colors for graphs with maximum degree Δ. It is easy to imagine that an algorithm which uses less colors in terms of Δ leads to an algorithm which uses less colors in terms of n. In this paper, we consider this influence assuming that we have an algorithm which uses Õ(Δ^1-x/k) colors for 2<x<3. Specifically, we will show that the algorithms of Karger et al., of Blum and Karger and of Halperin et al. can be improved under this assumption.},
 pages = {1046--1051},
 title = {On Approximation Algorithms for Coloring k-Colorable Graphs},
 volume = {E86-A},
 year = {2003}
}