Results 251 to 260 of about 446,387 (282)

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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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 a random tournament

Random Structures & Algorithms, 1995
AbstractThe number of Hamilton cycles in a random tournament is asymptotically normally distributed.
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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.
Colin Cooper, Alan M. Frieze, Michael Molloy 0001   +2 more
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On hamilton cycles and hamilton cycle decompositions of graphs based on groups [PDF]

A Hamilton cycle is a cycle which passes through every vertex of a graph. A Hamilton cycle decomposition of a k-regular graph is defined as the partition of the edge set into Hamilton cycles if k is even, or a partition into Hamilton cycles and a 1-factor, if k is odd.
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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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Packing of the k-power of Hamilton cycles

Discrete Mathematics
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Wanfang Chen, Changhong Lu, Qi Wu, Long-Tu Yuan   +3 more
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Spectral radius and the 2-power of Hamilton cycle

Discrete Mathematics, 2023
Xinru Yan, Xiaocong He, Lihua Feng
exaly  

The perfect matching and tight Hamilton cycle decomposition of complete n-balanced mk-partite k-uniform hypergraphs

Discrete Mathematics, 2023
Shunzhe Zhang, Chao Zhang
exaly  

Hamilton Cycles

2021
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