Equality of distance packing numbers.

We characterize the graphs for which the independence number equals the packing number. As a consequence we obtain simple structural descriptions of the graphs for which (i) the distance- k -packing number equals the distance- 2 k -packing number, and (ii) the distance- k -matching number equals the distance- 2 k -matching number. This last result considerably simplifies and extends previous results of Cameron and Walker (2005). For positive integers k 1 and k 2 with k 1 < k 2 and ⌈ ( 3 k 2 + 1 ) / 2 ⌉ ≤ 2 k 1 + 1 , we prove that it is NP-hard to determine for a given graph whether its distance- k 1 -packing number equals its distance- k 2 -packing number. [ABSTRACT FROM AUTHOR]