Edge-Packing in Planar Graphs

Maximum G Edge-Packing (EPack-sub G) is the problem of finding the maximum number of edge-disjoint isomorphic copies of a fixed guest graph G in a host graph H. This paper investigates the computational complexity of edge-packing for planar guests and planar hosts. Edge-packing is solvable in polynomial time when both G and H are either a 3-cycle or a k-star (graphs isomorphic to K(sub 1,k). Edge-packing is NP-complete when H is planar and G is either a cycle or a tree with greater than or equal to 3 edges. A strategy for developing polynomial-time approximation algorithms for planar hosts is exemplified by a linear-time approximation algorithm that finds a k-star edge-packing of size at least 1/2 optimal.