The strong isometric dimension of a graph G is the least number k such that G isometrically embeds into the strong product of k paths. Using Sperner’s Theorem, the strong isomet...
Abstract. In social network analysis, a k-clique is a relaxed clique, i.e., a kclique is a quasi-complete sub-graph. A k-clique in a graph is a sub-graph where the distance between...
An acyclic coloring of a graph is a proper vertex coloring such that the union of any two color classes induces a disjoint collection of trees. The more restricted notion of star ...
A 2-cover is a multiset of subsets of [n] := {1, 2, . . . , n} such that each element of [n] lies in exactly two of the subsets. A 2-cover is called proper if all of the subsets o...
We investigate the relationship between two kinds of vertex colorings of graphs: uniquemaximum colorings and conflict-free colorings. In a unique-maximum coloring, the colors are ...