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 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 constructing a tree directly. The algorithm also yields a 4/3-approximation for Minimum Connected Dominating Set in cubic graphs.

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