On the connectivity of radio networks

The connectivity of a two-dimensional radio network as a function of the range of the transmitters is still an open problem. It has bee conjectured that the critical range of this problem is the same as the one for the covering problem. The analysis of the one-dimensional problem makes it clear that situations can exist where these two ranges are different. It is conjectured that the critical ranges of the two-dimensional problems are also different. The author presents results to substantiate this conjecture