A set S V is a dominating set of a graph G = (V; E) if each vertex in V is either in S or is adjacent to a vertex in S. A vertex is said to dominate itself and all its neighbors. ...
Abstract. Feige and Kilian [5] showed that finding reasonable approximative solutions to the coloring problem on graphs is hard. This motivates the quest for algorithms that eithe...
Given a vector ( 1 2 ::: t) of non increasing positive integers, and an undirected graph G = (V E), an L( 1 2 ::: t)-coloring of G is a function f from the vertex set V to a set o...
Alan A. Bertossi, Maria Cristina Pinotti, Romeo Ri...
The first-fit chromatic number of a graph is the number of colors needed in the worst case of a greedy coloring. It is also called the Grundy number, which is defined to be the max...
Let G = (V, E) be a graph. Let c : V → N be a vertex-coloring of the vertices of G. For any vertex u, we denote by N[u] its closed neighborhood (u and its adjacent vertices), an...