Hamilton cycles and eigenvalues of graphs
نویسندگان
چکیده
منابع مشابه
Hamilton Cycles in Cubic Graphs
A graph is cubic if each of its vertex is of degree 3 and it is hamiltonian if it contains a cycle passing through all its vertices. It is known that if a cubic graph is hamiltonian, then it has at least three Hamilton cycles. This paper is about those works done concerning the number of Hamilton cycles in cubic graphs and related problems.
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We say that a k-uniform hypergraph C is an `-cycle if there exists a cyclic ordering of the vertices of C such that every edge of C consists of k consecutive vertices and such that every pair of adjacent edges (in the natural ordering of the edges) intersects in precisely ` vertices. We prove that if 1 ≤ ` < k and k − ` does not divide k then any k-uniform hypergraph on n vertices with minimum ...
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An n-lift of a graph K, is a graph with vertex set V (K)× [n] and for each edge (i, j) ∈ E(K) there is a perfect matching between {i} × [n] and {j} × [n]. If these matchings are chosen independently and uniformly at random then we say that we have a random n-lift. We show that there are constants h1, h2 such that if h ≥ h1 then a random n-lift of the complete graph Kh is hamiltonian whp and if ...
متن کاملPowers of Hamilton Cycles in Pseudorandom Graphs
We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph G is (ε, p, k, l)-pseudorandom if for all disjoint X and Y ⊆ V (G) with |X| ≥ εpkn and |Y | ≥ εpln we have e(X,Y ) = (1± ε)p|X||Y |. We prove that for all β > 0 there is an ε > 0 such that an (ε, p, 1, 2)-pseudorandom graph on n vertices with minim...
متن کاملEnumerating all Hamilton Cycles and Bounding the Number of Hamilton Cycles in 3-Regular Graphs
We describe an algorithm which enumerates all Hamilton cycles of a given 3regular n-vertex graph in time O(1.276n), improving on Eppstein’s previous bound. The resulting new upper bound of O(1.276n) for the maximum number of Hamilton cycles in 3-regular n-vertex graphs gets close to the best known lower bound of Ω(1.259n). Our method differs from Eppstein’s in that he considers in each step a n...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1995
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00254-o