On robust colorings of Hamming-distance graphs (Q1991409)

Summary: \(H_q(n,d)\) 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.