On Robust Colorings of Hamming-Distance Graphs
Keyword(s):
$H_q(n,d)$ is defined as the graph with vertex set $\mathbb{Z}_q^n$ 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 $H_2(n,n-1)$ 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 $H_2(n,n-1)$ is presented.
Keyword(s):
Keyword(s):
2012 ◽
Vol 12
(03)
◽
pp. 1250179
◽
2021 ◽
Vol 33
(5)
◽
pp. 66-73
Keyword(s):
Keyword(s):
2015 ◽
Vol 14
(06)
◽
pp. 1550079
◽
Keyword(s):
2012 ◽
Vol 25
(4)
◽
pp. 680-693
◽
Keyword(s):