منابع مشابه
Hamiltonian Square Roots of Skew-Hamiltonian Matrices
We present a constructive existence proof that every real skew-Hamiltonian matrix W has a real Hamiltonian square root. The key step in this construction shows how one may bring any such W into a real quasi-Jordan canonical form via symplectic similarity. We show further that every W has infinitely many real Hamiltonian square roots, and give a lower bound on the dimension of the set of all suc...
متن کاملHamiltonian Spectra of Trees
Let G be a connected graph, and let d(u, v) denote the distance between vertices u and v in G. For any cyclic ordering π of V (G), π = (v1, v2, · · · , vn, vn+1) where vn+1 = v1, let d(π) = n ∑ i=1 d(vi, vi+1). The set of possible values of d(π) over all cyclic orderings π of V (G) is called the Hamiltonian spectrum of G. We determine the Hamiltonian spectrum for any tree.
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For a connected graph, a path containing all vertices is known as Hamiltonian path. For general graphs, there is no known necessary and sufficient condition for the existence of Hamiltonian paths and the complexity of finding a Hamiltonian path in general graphs is NP-Complete. We present a necessary and sufficient condition for the existence of Hamiltonian paths in 2-trees. Using our character...
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A set S ⊆ V is a global dominating set of a graph G = (V,E) if S is a dominating set of G and G, where G is the complement graph of G. The global domination number γg(G) equals the minimum cardinality of a global dominating set of G. The square graph G of a graph G is the graph with vertex set V and two vertices are adjacent in G if they are joined in G by a path of length one or two. In this p...
متن کاملWeak Square Sequences and Special Aronszajn Trees
A classical theorem of set theory is the equivalence of the weak square principle μ with the existence of a special Aronszajn tree on μ +. We introduce the notion of a weak square sequence on any regular uncountable cardinal, and prove that the equivalence between weak square sequences and special Aronszajn trees holds in general. Recall the weak square principle μ for an infinite cardinal μ, w...
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ژورنال
عنوان ژورنال: Mathematika
سال: 1971
ISSN: 0025-5793,2041-7942
DOI: 10.1112/s0025579300008494