On Approximation Algorithms for Coloring k-Colorable Graphs

Xuzhen XIE, Takao ONO, Tomio HIRATA

Summary :

Karger, Motwani and Sudan presented a graph coloring algorithm based on semidefinite programming, which colors any k-colorable graph with maximum degree Δ using (Δ^1-2/k) colors. This algorithm leads to an algorithm for k-colorable graph using (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 (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.

• Publication: IEICE TRANSACTIONS on Fundamentals Vol.E86-A No.5 pp.1046-1051
• Publication Date: 2003/05/01
• Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)

Authors

Xuzhen XIE
Takao ONO
Tomio HIRATA

Keyword

graph coloring,  approximation algorithms,  NP-hard,  maximum degree