Complexity of the maximum leaf spanning tree problem on planar and regular graphs

In this paper, we consider the problem of finding a spanning tree in a graph that maximizes the number of leaves. We show the NP -hardness of this problem for graphs that are planar and cubic. Our proof will be an adaption of the proof for arbitrary cubic graphs in Lemke (1988) 9. Furthermore, it is shown that the problem is APX -hard on 5-regular graphs. Finally, we extend our proof to k-regular graphs for odd k 5 .

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