We study the computational complexity of several problems connected with
finding a maximal distance-k matching of minimum cardinality or minimum
weight in a given graph. We introduce the class of k-equimatchable graphs
which is an edge analogue of k-equipackable graphs. We prove that the
recognition of k-equimatchable graphs is co-NP-complete for any fixed kβ₯2. We provide a simple characterization for the class of strongly chordal
graphs with equal k-packing and k-domination numbers. We also prove that
for any fixed integer ββ₯1 the problem of finding a minimum weight
maximal distance-2β matching and the problem of finding a minimum weight
(2ββ1)-independent dominating set cannot be approximated in polynomial
time in chordal graphs within a factor of Ξ΄lnβ£V(G)β£ unless
P=NP, where Ξ΄ is a fixed constant (thereby
improving the NP-hardness result of Chang for the independent domination case).
Finally, we show the NP-hardness of the minimum maximal induced matching and
independent dominating set problems in large-girth planar graphs.Comment: 15 pages, 4 figure