It was shown by Griggs and Wu that a graph of minimal degree 4 on n vertices has a spanning tree with at least $$ \frac{2}{5} $$
 n leaves, which is asymptomatically the best possible bound for this class of graphs. In this paper, we present a polynomial time algorithm that finds in any graph with k vertices of degree greater than or equal to 4 and k′ vertices of degree 3 a spanning tree with $$ \left[ {\frac{2}{5} \cdot k + \frac{2}{{15}} \cdot k'} \right] $$
 leaves.

Finding a spanning tree of a graph with maximal number of terminal vertices.

Constructing a spanning tree with many leaves

Horn's algorithm for weighted mean flow scheduling with treelike precedence constraints is reexamined. A new analysis of an efficient implementation of Horn's algorithm shows an O(n log n) complexity. This is an improvement on the known O(n2) complexity of this algorithm. An application of Horn's algorithm to a problem of optimal scheduling of a treelike communication network is presented.

Mean flow scheduling and optimal construction of a treelike communication network

Остовное дерево с большим числом висячих вершин@@@A spanning tree with a large number of pendant vertices

We prove that for every connected graph G( V, E) with no adjacent vertices of degree 2 there exists a spanning tree with more than | V|/5 end vertices. We describe a polynomial algorithm of constructing such a tree. The constant 1/5 cannot be improved.

Finding a spanning tree of a graph with maximal number of terminal vertices.

Citations

Constructing a spanning tree with many leaves

Mean flow scheduling and optimal construction of a treelike communication network

Остовное дерево с большим числом висячих вершин@@@A spanning tree with a large number of pendant vertices

Spanning trees with large number of end vertices

Related Papers (5)

Vertex-disjoint cycles containing specified edges in a bipartite graph

Complexity of Computing the Expected Maximum Number of Edge-Disjoint s-t Paths on Probabilistic Graphs.

Parallel top-k subgraph query in massive graphs: Computing from the perspective of single vertex

A note on “A linear-size zero-one programming model for the minimum spanning tree problem in planar graphs”

Limiting shape of the depth first search tree in an Erdős-Rényi graph