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Preprints 2008

A 3/2-approximation algorithm for finding spanning trees with many leaves in cubic graphs
Zitatschlüssel Report-015-2008
Autor Paul Bonsma and Florian Zickfeld
Jahr 2008
Nummer 015
Notiz Submitted.
Institution Technische Universität Berlin, Institut für Mathematik
Zusammenfassung 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.
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