Abstract:
Packing and Covering are some of the fundamental problems in graph theory. An H-
P ACKING problem is, given a graph G, what is the maximum number of disjoint graphs in
H one can find in G. Similarly in H-C OVERING problem we desire to find the minimum
number of disjoint graphs in H that together constitute the graph G. Both these problems
are extremely well studied and proved to be NP-hard. The C OVERING problems that we
study encompasses the very well known H AMILTONICITY problems. In part 1 of our thesis
we study these problems where H is the class of cycles/paths. We study these problems
with respect to the standard parameter (solution size) as well as some well known structural
parameter