A note on balanced colourings for lattice points
Discrete Mathematics
A sufficient condition for equitable edge-colourings of simple graphs
Discrete Mathematics
Handbook of combinatorics (vol. 2)
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Balanced Coloring: Equally Easy for All Numbers of Colors?
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
| Hi-index | 0.00 |
While discrepancy theory is normally only studied in the context of 2-colorings, we explore the problem of k-coloring, for k ≥ 2, a set of vertices to minimize imbalance among a family of subsets of vertices. The imbalance is the maximum, over all subsets in the family, of the largest difference between the size of any two color classes in that subset. The discrepancy is the minimum possible imbalance. We show that the discrepancy is always at most 4d-3, where d (the "dimension") is the maximum number of subsets containing a common vertex. For 2- colorings, the bound on the discrepancy is at most max{2d-3, 2}. Finally, we prove that several restricted versions of computing the discrepancy are NP-complete.