منابع مشابه
Vertices Belonging to All or to No Minimum Locating Dominating Sets of Trees
A set D of vertices in a graph G is a locating-dominating set if for every two vertices u, v of G \ D the sets N(u) ∩ D and N(v) ∩ D are non-empty and different. In this paper, we characterize vertices that are in all or in no minimum locating dominating sets in trees. The characterization guarantees that the γL-excellent tree can be recognized in a polynomial time.
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We present tight bounds on splitting trees into “small” subtrees.
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We prove a conjecture of Horak that can be thought of as an extension of classical results including Dirac’s theorem on the existence of Hamiltonian cycles. Namely, we prove for 1 ≤ k ≤ n − 2 if G is a connected graph with A ⊂ V (G) such that dG(v) ≥ k for all v ∈ A, then there exists a subtree T of G such that V (T ) ⊃ A and dT (v) ≤ ⌈ n−1 k ⌉ for all v ∈ A.
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We study the paramereteized complexity of the following connectivity problem. For a vertex subset U of a graph G, trees T1, . . . , Ts of G are completely independent spanning trees of U if each of them contains U , and for every two distinct vertices u, v ∈ U , the paths from u to v in T1, . . . , Ts are pairwise vertex disjoint except for end-vertices u and v. Then for a given s ≥ 2 and a par...
متن کاملStrongly simplicial vertices of powers of trees
For a tree T and an integer k 1, it is well known that the kth power T k of T is strongly chordal and hence has a strong elimination ordering of its vertices. In this note we obtain a complete characterization of strongly simplicial vertices of T k , thereby characterizing all strong elimination orderings of the vertices of T k . © 2007 Elsevier B.V. All rights reserved.
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1970
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093894009