Results 301 to 310 of about 3,218,251 (319)

Polychromatic Hamilton cycles

1991
Abstract: "The edges of the complete graph K[subscript n] are coloured so that no colour appears no more than k times, k = [n/A 1n n], for some sufficiently large A. We show that there is always a Hamiltonian cycle in which each edge is a different colour. The proof technique is probabilistic."
Frieze, Reed, Bruce A.
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On Hamilton cycles in Erdős‐Rényi subgraphs of large graphs

Random Struct. Algorithms, 2020
Given a graph Γn=(V,E) on n vertices and m edges, we define the Erdős‐Rényi graph process with host Γn as follows. A permutation e1,…,em of E is chosen uniformly at random, and for t ≤ m we let Γn,t=(V,{e1,…,et}). Suppose the minimum degree of Γn is δ(Γn)
T. Johansson
semanticscholar   +1 more source

Hamilton cycles in prisms

Journal of Graph Theory, 2007
AbstractThe prism over a graph G is the Cartesian product G □ K2 of G with the complete graph K2. If G is hamiltonian, then G□K2 is also hamiltonian but the converse does not hold in general. Having a hamiltonian prism is shown to be an interesting relaxation of being hamiltonian.
Kaiser, Tomáš, Ryjáček, Zdeněk, Král, Daniel, Rosenfeld, Moshe, Voss, Heinz-Jürgen   +4 more
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Neighborhood unions and hamilton cycles

Journal of Graph Theory, 1991
AbstractLet G be a graph on n vertices and N2(G) denote the minimum size of N(u) ∪ N(v) taken over all pairs of independent vertices u, v of G. We show that if G is 3‐connected and N2(G) ⩾ ½(n + 1), then G has a Hamilton cycle. We show further that if G is 2‐connected and N2(G) ⩾ ½(n + 3), then either G has a Hamilton cycle or else G belongs to one of ...
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Hamilton Cycles in Oriented Graphs

Combinatorics, Probability and Computing, 1993
It is shown that an oriented graph of order n whose every indegree and outdegree is at least cn is hamiltonian if c ≥ ½ − 2−15 but need not be if c < ⅜.
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Hamilton Cycles and Paths in Fullerenes

Journal of Chemical Information and Modeling, 2007
AbstractChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract, please click on HTML or PDF.
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Hamilton Cycles in Random Regular Digraphs

Combinatorics, Probability and Computing, 1994
We prove that almost every r-regular digraph is Hamiltonian for all fixed r ≥ 3.
Cooper, Colin, Frieze, Alan, Molloy, Michael   +2 more
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The Hamilton‐Waterloo problem for Hamilton cycles and triangle‐factors

Journal of Combinatorial Designs, 2011
AbstractIn this article, we consider the Hamilton‐Waterloo problem for the case of Hamilton cycles and triangle‐factors when the order of the complete graph Kn is even. We completely solved the problem for the case n≡24 (mod 36). For the cases n≡0 (mod 18) and n≡6 (mod 36), we gave an almost complete solution. © 2012 Wiley Periodicals, Inc. J.
Lei, Hongchuan, Shen, Hao
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Hamilton cycles in claw‐free graphs

Journal of Graph Theory, 1988
AbstractBondy conjectured that if G is a k‐connected graph of order n such that magnified image for any (k + 1)‐independent set / of G, then the subgraph outside any longest cycle contains no path of length k − 1. In this paper, we are going to prove that, if G is a k‐connected claw‐free (K1,3‐free) graph of order n such that magnified image for any (k
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Hamilton cycles in plane triangulations

Journal of Graph Theory, 2002
AbstractWe extend Whitney's Theorem that every plane triangulation without separating triangles is hamiltonian by allowing some separating triangles. More precisely, we define a decomposition of a plane triangulation G into 4‐connected ‘pieces,’ and show that if each piece shares a triangle with at most three other pieces then G is hamiltonian.
Jackson, Bill, Yu, Xingxing
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