Results 11 to 20 of about 60,523 (284)
Discrete Mathematics, 1993 AbstractThe edges of the complete graph Kn are coloured so that no colour appears more than k=k(n) times, k=⌈n(A ln 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.
Alan Frieze, Bruce H. Reed
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Packing Hamilton Cycles Online [PDF]
Combinatorics, Probability and Computing, 2018 It is known that w.h.p. the hitting time τ2σ for the random graph process to have minimum degree 2σ coincides with the hitting time for σ edge-disjoint Hamilton cycles [4, 9, 13]. In this paper we prove an online version of this property. We show that, for a fixed integer σ ⩾ 2, if random edges of Kn are presented one by one then w.h.p.
Briggs, Joseph +4 more
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Rainbow hamilton cycles in random graphs [PDF]
Random Structures & Algorithms, 2013 AbstractOne of the most famous results in the theory of random graphs establishes that the threshold for Hamiltonicity in the Erdős‐Rényi random graph Gn,p is around . Much research has been done to extend this to increasingly challenging random structures.
Alan Frieze, Po-Shen Loh
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Powers of Hamilton cycles in pseudorandom graphs [PDF]
Combinatorica, 2014 30 pages, 1 ...
Allen, Peter +4 more
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Hamilton cycles in digraphs of unitary matrices
Discrete Mathematics, 2006 A set $S\subseteq V$ is called an {\em $q^+$-set} ({\em $q^-$-set}, respectively) if $S$ has at least two vertices and, for every $u\in S$, there exists $v\in S, v\neq u$ such that $N^+(u)\cap N^+(v)\neq \emptyset$ ($N^-(u)\cap N^-(v)\neq \emptyset$, respectively). A digraph $D$ is called {\em s-quadrangular} if, for every $q^+$-set $S$, we have $|\cup
Anders Yeo +3 more
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On the Resilience of Hamiltonicity and Optimal Packing of Hamilton Cycles in Random Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2011 Let $\bk=(k_1,...,k_n)$ be a sequence of $n$ integers. For an increasing monotone graph property $\mP$ we say that a base graph $G=([n],E)$ is \emph{$\bk$-resilient} with respect to $\mP$ if for every subgraph $H\subseteq G$ such that $d_H(i)\leq k_i$ for every $1\leq i\leq n$ the graph $G-H$ possesses $\mP$.
Sonny Ben-Shimon +2 more
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Powers of Hamilton cycles in random graphs and tight Hamilton cycles in random hypergraphs [PDF]
Random Structures & Algorithms, 2018 AbstractWe show that for every there exists C > 0 such that if then asymptotically almost surely the random graph contains the kth power of a Hamilton cycle. This determines the threshold for appearance of the square of a Hamilton cycle up to the logarithmic factor, improving a result of Kühn and Osthus.
Nemanja Škorić, Rajko Nenadov
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A survey on Hamilton cycles in directed graphs
European Journal of Combinatorics, 2012 We survey some recent results on long-standing conjectures regarding Hamilton cycles in directed graphs, oriented graphs and tournaments. We also combine some of these to prove the following approximate result towards Kelly's conjecture on Hamilton decompositions of regular tournaments: the edges of every regular tournament can be covered by a set of ...
Daniela Kühn, Deryk Osthus
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A new algorithm to find fuzzy Hamilton cycle in a fuzzy network using adjacency matrix and minimum vertex degree [PDF]
Springerplus, 2016 A. Nagoor Gani, S. R. Latha
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Hamilton Cycles in Infinite Cubic Graphs
The Electronic Journal of Combinatorics, 2018 Investigating a problem of B. Mohar, we show that every one-ended Hamiltonian cubic graph with end degree 3 contains a second Hamilton cycle. We also construct two examples showing that this result does not extend to give a third Hamilton cycle, nor that it extends to the two-ended case.
Max Pitz
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