Spanning trees with many leaves
SIAM Journal on Discrete Mathematics
Spanning trees in graphs of minimum degree 4 or 5
Discrete Mathematics
A short note on the approximability of the maximum leaves spanning tree problem
Information Processing Letters
Approximating maximum leaf spanning trees in almost linear time
Journal of Algorithms
Connected Domination and Spanning Trees with Many Leaves
SIAM Journal on Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Linear Time Minor Tests and Depth First Search
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Approximation Algorithm for the Maximum Leaf Spanning Tree Problem for Cubic Graphs
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
The Power of Local Optimizations: Approximation Algorithms for Maximun-leaf Spanning Tree (DRAFT)*
The Power of Local Optimizations: Approximation Algorithms for Maximun-leaf Spanning Tree (DRAFT)*
Spanning trees with many leaves
Journal of Graph Theory
Complexities of some interesting problems on spanning trees
Information Processing Letters
Variations of the maximum leaf spanning tree problem for bipartite graphs
Information Processing Letters
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Given a d-regular bipartite graph Gd, whose nodes are divided in black nodes and white nodes according to the partition, we consider the problem of computing the spanning tree of Gd with the maximum number of black leaves. We prove that the problem is NP hard for any fixed d ≥ 4 and we present a simple greedy algorithm that gives a constant approximation ratio for the problem. More precisely our algorithm can be used to get in linear time an approximation ratio of 2 - 2/(d - 1)2 for d ≥ 4. When applied to cubic bipartite graphs the algorithm only achieves a 2-approximation ratio. Hence we introduce a local optimization step that allows us to improve the approximation ratio for cubic bipartite graphs to 1.5. Focusing on structural properties, the analysis of our algorithm proves a lower bound on lB(n, d), i.e., the minimum m such that every Gd with n black nodes has a spanning tree with at least m black leaves. In particular, for d = 3 we prove that lB(n, 3) is exactly ⌈n/3⌉ +1.