We study the computational complexity of several problems connected with the problems of finding a maximal distance-k matching of minimum cardinality or minimum weight. 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 k ≥ 2. We provide a simple characteriza...

Recent research in frequent pattern mining (FPM) has shifted from obtaining the complete set of frequent patterns to generating only a representative (summary) subset of frequent patterns. Most of the existing approaches to this problem adopt a two-step solution; in the first step, they obtain all the frequent patterns, and in the second step, some form of clustering is used to obtain the summa...

The integer k is allowed to vary with n at a rate not exceeding log n. We obtain laws of the iterated logarithm for all the k's in the given range. For small k, the methods used in the proofs are borrowed from extreme value theory. For larger k, the techniques are reminiscent of those used in the proof of the Erd/Ss-Rdnyi theorem.

A graph is k-degenerate if its vertices can be successively deleted so that when deleted, each has degree at most k. These graphs were introduced by Lick and White in 1970 and have been studied in several subsequent papers. We present sharp bounds on the diameter of maximal k-degenerate graphs and characterize the extremal graphs for the upper bound. We present a simple characterization of the ...