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In this paper, we consider whether the vertices of graph G can be partitioned into K subsets V 1, V 2, ... V K so that for each i 驴 {1,...,K}, the subgraph induced by V i is a perfect matching where K ≤ 驴 V 驴. It is known that it is an NP complete problem in general graphs. In this paper, we restrict the problem in Halin graphs and give an algorithm to find the minimum value of K (2 ≤ K ≤ 4) in Halin graphs. The time complexity is O(n).

An Algorithm to Solve the Partition into Perfect Matchings Problem in Halin Graphs