A k-tuple coloring of a graph G assigns a set of k colors to each vertex of G such that if two vertices are adjacent, the corresponding sets of colors are disjoint. The k-tuple chromatic number of G, χk(G), is the smallest ...

In the (k, i)-coloring problem, we aim to assign sets of colors of size k to the vertices of a graph G, so that the sets which belong to adjacent vertices of G intersect in no more than i elements and the total number of ...

In the (k,i)-coloring problem, we aim to assign sets of colors of size k to the vertices of a graph G, so that the sets which belong to adjacent vertices of G intersect in no more than i elements and the total number of ...

Let n, k, r be positive integers, with n ≥ kr. The r-uniform Kneser hypergraph KGr(n, k) has as vertex set the set of all k-subsets of the set {1,…,n} and its (hyper) edges are formed by the r-tuples of pairwise disjoint ...