In this article, we study the (k,c)-coloring problem, a generalization of the vertex coloring problem where we have to assign k colors to each vertex of an undirected graph, and two adjacent vertices can share at most c ...

An edge coloring is an assignment of colors to the edges of a graph G such that edges that are incident to the same vertex receive distinct colors. Given an edge coloring of a graph G, the color-set of a vertex V is the ...

Confirming a conjecture of Gyarfas, we prove that, for all natural numbers k and r, the vertices of every r-edge-colored complete k-uniform hypergraph can be partitioned into a bounded number (independent of the size of ...

An adjacent vertex distinguishing total coloring is a coloring on the vertices and edges of a graph such that adjacent edges and its common vertex have distinguishing colors, and for every two adjacent vertices their ...

Two elements of a graph are adjacent if they are the vertices of an edge, or if they are two edges which share a common vertex, or if they are an edge and one of its vertices. A coloring of a graph is an assignment of ...