منابع مشابه
Spanning directed trees with many leaves
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 – every strongly connected n-vertex digraph D with minimum indegree at least 3 has an out-branching with at least (n/4) −...
متن کاملOn Finding Directed Trees with Many Leaves
The Rooted Maximum Leaf Outbranching problem consists in finding a spanning directed tree rooted at some prescribed vertex of a digraph with the maximum number of leaves. Its parameterized version asks if there exists such a tree with at least $k$ leaves. We use the notion of $s-t$ numbering to exhibit combinatorial bounds on the existence of spanning directed trees with many leaves. These comb...
متن کاملConnected Domination and Spanning Trees with Many Leaves
Let G = (V,E) be a connected graph. A connected dominating set S ⊂ V is a dominating set that induces a connected subgraph of G. The connected domination number of G, denoted γc(G), is the minimum cardinality of a connected dominating set. Alternatively, |V | − γc(G) is the maximum number of leaves in a spanning tree of G. Let δ denote the minimum degree of G. We prove that γc(G) ≤ |V | ln(δ+1)...
متن کاملSpanning Trees with Many Leaves and Average Distance
In this paper we prove several new lower bounds on the maximum number of leaves of a spanning tree of a graph related to its order, independence number, local independence number, and the maximum order of a bipartite subgraph. These new lower bounds were conjectured by the program Graffiti.pc, a variant of the program Graffiti. We use two of these results to give two partial resolutions of conj...
متن کاملSpanning Trees with Many Leaves in Regular Bipartite Graphs
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 ou...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2009
ISSN: 0895-4801,1095-7146
DOI: 10.1137/070710494