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...
An arc of a graph is an oriented edge and a 3-arc is a 4-tuple (v, u, x, y) of vertices such that both (v, u, x) and (u, x, y) are paths of length two. The 3-arc graph of a graph ...
Let P be a family of dipaths. The load of an arc is the number of dipaths containing this arc. Let π(G, P) be the maximum of the load of all the arcs and let w(G, P) be the minim...
Given a graph G = (V, E) and positive integral vertex weights w : V → N, the max-coloring problem seeks to find a proper vertex coloring of G whose color classes C1, C2, . . . ,...
A cellular network is generally modeled as a subgraph of the triangular lattice. In the static frequency assignment problem, each vertex of the graph is a base station in the netw...