@article{5ae7f652d1aa44af8e5aa448bf254429,

title = "Spanning directed trees with many leaves",

abstract = "The DIRECTED MAXIMUM LEAF OUT-BRANCHING problem is to find an out-branching (i.e., a rooted oriented spanning tree) in a given digraph with the maximum number of leaves. In this paper, we obtain two combinatorial results on the number of leaves in out-branchings. We show that (1) every strongly connected n-vertex digraph D with minimum in-degree at least 3 has an outbranching with at least (n/4)1/3 - 1 leaves; (2) if a strongly connected digraph D does not contain an out-branching with k leaves, then the pathwidth of its underlying graph UG(D) is O(k log k), and if the digraph is acyclic with a single vertex of in-degree zero, then the pathwidth is at most 4k. The last result implies that it can be decided in time 2O(k log2 k) · nO(1) whether a strongly connected digraph on n vertices has an out-branching with at least k leaves. On acyclic digraphs the running time of our algorithm is 2O(k log k) · nO(1).",

keywords = "Directed graphs, Fixed parameter tractability, Maximum leaf, Out-branching, Rooted tree",

author = "Noga Alon and Fomin, {Fedor V.} and Gregory Gutin and Michael Krivelevich and Saket Saurabh",

year = "2008",

doi = "10.1137/070710494",

language = "אנגלית",

volume = "23",

pages = "466--476",

journal = "SIAM Journal on Discrete Mathematics",

issn = "0895-4801",

publisher = "Society for Industrial and Applied Mathematics (SIAM)",

number = "1",

}