Bonsma, PaulZickfeld, Florian2021-12-172021-12-1720082197-8085https://depositonce.tu-berlin.de/handle/11303/15645http://dx.doi.org/10.14279/depositonce-14418We 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.en510 Mathematikspanning treemax leafapproximationcubic graphResearch Paper