Hq(n, d) is defined as the graph with vertex set Znq and where two vertices are adjacent if their Hamming distance is at least d. The chromatic number of these graphs is presented for various sets of parameters (q, n, d). For the 4-colorings of the graphs H2(n, n − 1) a notion of robustness is introduced. It is based on the tolerance of swapping colors along an edge without destroying properness of the coloring. An explicit description of the maximally robust 4-colorings of H2 (n, n − 1) is presented.

Document Type


Publication Date


Notes/Citation Information

Published in The Electronic Journal of Combinatorics, v. 25, issue 4, paper #P4.3, p. 1-22.

© The authors.

Released under the CC BY-ND license (International 4.0).

Funding Information

HGL was partially supported by the National Science Foundation Grant DMS-1210061.

Included in

Mathematics Commons