Coloring random and semi-random k-colorable graphs
Journal of Algorithms
A Spectral Technique for Coloring Random 3-Colorable Graphs
SIAM Journal on Computing
Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Zero knowledge and the chromatic number
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Heuristics for semirandom graph problems
Journal of Computer and System Sciences
New approximation guarantee for chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Conditional hardness for approximate coloring
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Combinatorics, Probability and Computing
| Hi-index | 0.89 |
As part of the efforts to understand the intricacies of the k-colorability problem, different distributions over k-colorable graphs have been analyzed. While the problem is notoriously hard (not even reasonably approximable) in the worst case, the average case (with respect to such distributions) often turns out to be ''easy''. Semi-random models mediate between these two extremes and are more suitable to imitate ''real-life'' instances than purely random models. In this work we consider semi-random variants of the planted k-colorability distribution. This continues a line of research pursued by Coja-Oghlan, and by Krivelevich and Vilenchik. Our aim is to study a more general semi-random framework than those suggested so far. On the one hand we show that previous algorithmic techniques extend to our more general semi-random setting; on the other hand we give a hardness result, proving that a closely related semi-random model is intractable. Thus we provide some indication about which properties of the input distribution make the k-colorability problem hard.