Heuristic method to determine lucky k-polynomials for k-colorable graphs

Bipartite, k-Colorable and k-Colored Graphs

Coloring k-colorable graphs using smaller palettes

We obtain the following new coloring results: A 3-colorable graph on n vertices with maximum degree can be colored, in polynomial time, us

Almost All k-Colorable Graphs are Easy to Color

We describe a simple and eecient heuristic algorithm for the graph coloring problem and show that for all k 1, it nds an optimal coloring for almost all k-colorable graphs. We also show that an algorithm proposed by Br elaz and justiied on experimental grounds optimally colors almost all k-colorable graphs. EEcient implementations of both algorithms are given. The rst one runs in O(n+m log k) t...

On Approximation Algorithms for Coloring k-Colorable Graphs

Karger, Motwani and Sudan presented a graph coloring algorithm based on semidefinite programming, which colors any k-colorable graph with maximum degree ∆ using Õ(∆1−2/k) colors. This algorithm leads to an algorithm for k-colorable graph using Õ(n1−3/(k+1)) colors. This improved Wigderson’s algorithm, which uses O(n1−1/(k−1)) colors, containing as a subroutine an algorithm using (∆ + 1) colors ...

Coloring Sparse Random k-Colorable Graphs in Polynomial Expected Time

Feige and Kilian [5] showed that finding reasonable approximative solutions to the coloring problem on graphs is hard. This motivates the quest for algorithms that either solve the problem in most but not all cases, but are of polynomial time complexity, or that give a correct solution on all input graphs while guaranteeing a polynomial running time on average only. An algorithm of the first ki...