Maximal ambiguously 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

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...

Coloring Random and Semi-Random k-Colorable Graphs

The problem of coloring a graph with the minimum number of colors is well known to be NPhard, even restricted to k-colorable graphs for constant k 3. On the other hand, it is known that random k-colorable graphs are easy to k-color. The algorithms for coloring random kcolorable graphs require fairly high edge densities, however. In this paper we present algorithms that color randomly generated ...

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...