An $$O^{*}(1.4366^n)$$O∗(1.4366n)-time exact algorithm for maximum $$P_2$$P2-packing in cubic graphs

Given a graph $$G=(V, E)$$G=(V,E), a $$P_2$$P2-packing$$\mathcal {P}$$P is a collection of vertex disjoint copies of $$P_2$$P2s in $$G$$G where a $$P_2$$P2 is a simple path with three vertices and two edges. The Maximum$$P_2$$P2-Packing problem is to find a $$P_2$$P2-packing $$\mathcal {P}$$P in the input graph $$G$$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$$P_2$$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 $$O^{*}(1.4366^n)$$O∗(1.4366n) which is faster than previous known exact algorithms where $$n$$n is the number of vertices in the input graph.