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

Paul Bonsma, Florian Zickfeld
2008 Lecture Notes in Computer Science  
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
more » ... 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.
doi:10.1007/978-3-540-92248-3_7 fatcat:3pixexls7vh6dopbe3lfe53ssy