A 3/2-Approximation Algorithm for Finding Spanning Trees with Many Leaves in Cubic Graphs

We consider the problem of finding a spanning tree that maximizes the number of leaves (MaxLeaf). We provide a 3/2-approximation algorithm for this problem when restricted to cubic graphs, improving on the previous 5/3-approximation for this class. To obtain this approximation we define a graph parameter $x(G)$ and construct a tree with at least $(n-x(G)+4)/3$ leaves, and we prove that no tree with more than $(n-x(G)+2)/2$ leaves exists. In contrast to previous approximation algorithms for MaxLeaf, our algorithm works with connected dominating sets instead of by constructing a tree directly. The algorithm also yields a 4/3-approximation for the minimum connected dominating set problem in cubic graphs.

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