منابع مشابه
Hamiltonian Paths in the Square of a Tree
We introduce a new family of graphs for which the Hamiltonian path problem is non-trivial and yet has a linear time solution. The square of a graph G = (V, E), denoted as G, is a graph with the set of vertices V , in which two vertices are connected by an edge if there exists a path of length at most 2 connecting them in G. Harary & Schwenk (1971) proved that the square of a tree T contains a H...
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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...
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A Hamiltonian cycle is a spanning cycle in a graph, i.e., a cycle through every vertex, and a Hamiltonian path is a spanning path. In this paper we present two theorems stating sufficient conditions for a graph to possess Hamiltonian cycles and Hamiltonian paths. The significance of the theorems is discussed, and it is shown that the famous Ore’s theorem directly follows from our result. 2004...
متن کاملAbsolute Differences Along Hamiltonian Paths
We prove that if the vertices of a complete graph are labeled with the elements of an arithmetic progression, then for any given vertex there is a Hamiltonian path starting at this vertex such that the absolute values of the differences of consecutive vertices along the path are pairwise distinct. In another extreme case where the label set has small additive energy, we show that the graph actu...
متن کاملCounting Hamiltonian Paths of Tournaments
It is well known that every tournament has a directed path containing all the vertices of V , i.e. a hamiltonian path. It is an easy exercise to show that a tournament has a unique such path if and only if the arcs of A induce a transitive relation on V . In this paper we show that by reversing the arcs of the hamiltonian path in a transitive tournament with n vertices we obtain a tournament wi...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1996
ISSN: 0095-8956
DOI: 10.1006/jctb.1996.0039