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A 3/2-approximation algorithm for finding spanning trees with many leaves in cubic graphs

Bonsma, Paul; Zickfeld, Florian

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

We consider the problem of finding a spanning tree that maximizes the number of leaves (Max Leaf). 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 Max Leaf, 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.