Computational problems in graph theory | NP-hard problems | NP-complete problems | Extensions and generalizations of graphs | Graph coloring
Radio coloring
In graph theory, a branch of mathematics, a radio coloring of an undirected graph is a form of graph coloring in which one assigns positive integer labels to the graphssuch that the labels of adjacent vertices differ by at least two, and the labels of vertices at distance two from each other differ by at least one. Radio coloring was first studied by , under a different name, L(2,1)-labeling. It was called radio coloring by Frank Harary because it models the problem of channel assignment in radio broadcasting, while avoiding electromagnetic interference between radio stations that are near each other both in the graph and in their assigned channel frequencies. The span of a radio coloring is its maximum label, and the radio coloring number of a graph is the smallest possible span of a radio coloring. For instance, the graph consisting of two vertices with a single edge has radio coloring number 3: it has a radio coloring with one vertex labeled 1 and the other labeled 3, but it is not possible for a radio coloring of this graph to use only the labels 1 and 2. (Wikipedia).
