Given a graph G = (V, E), a P2-packing [Pscr ] is a collection of vertex disjoint copies of P2s in G where a P2 is a simple path with three vertices and two edges. The MAXIMUM P2-PACKING problem is to find a P2-packing [Pscr ] in the input graph G of maximum cardinality. This problem is NP-hard for cubic graphs. In this paper, we give a branch-and-reduce algorithm for the MAXIMUM P2-PACKING problem in cubic graphs. We analyze the running time of the algorithm using measure-and-conquer and show that it runs in time O*(1.4366n) which is faster than previous known exact algorithms where n is the number of vertices in the input graph.
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