L(2, 1)-Coloring Matrogenic Graphs

This paper investigates a variant of the general problem of assigning channels to the stations of a wireless network when the graph representing the possible interferences is a matrogenic graph. In this problem, channels assigned to adjacent vertices must be at least two apart, while the same channel can be reused for vertices whose distance is at least three. Linear time algorithms are provided for matrogenic graphs and, in particular, for two specific subclasses: threshold graphs and split matrogenic graphs. For the first one of these classes the algorithm is exact, while for the other ones it approximates the optimal solution. Consequently, improvements on previously known results concerning subclasses of cographs, split graphs and graphs with diameter two are achieved.