Name
Abstract | ||
|---|---|---|
A cube-like graph is a Cayley graph for the elementary abelian group of order 2(n). In studies of the chromatic number of cube-like graphs, the kth power of the n-dimensional hypercube, Q(n)(k), is frequently considered. This coloring problem can be considered in the framework of coding theory, as the graph Q(n)(k) can be constructed with one vertex for each binary word of length n and edges between vertices exactly when the Hamming distance between the corresponding words is at most k. Consequently, a proper coloring of Q(n)(k) corresponds to a partition of the n-dimensional binary Hamming space into codes with minimum distance at least k + 1. The smallest open case, the chromatic number of Q(8)(2), is here settled by finding a 13-coloring. Such 13-colorings with specific symmetries are further classified. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1090/mcom/3291 | MATHEMATICS OF COMPUTATION |
DocType | Volume | Issue |
Journal | 87 | 313 |
ISSN | Citations | PageRank |
0025-5718 | 0 | 0.34 |
References | Authors | |
10 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Janne I. Kokkala | 1 | 9 | 2.46 |
| Patric R. J. Östergård | 2 | 609 | 70.61 |