Results 21 to 30 of about 3,567,425 (361)
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
Gregory Gutin +3 more
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Powers of Hamilton cycles in random graphs and tight Hamilton cycles in random hypergraphs [PDF]
Random Structures & Algorithms, 2016 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.
Rajko Nenadov, Nemanja Škorić
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A survey on Hamilton cycles in directed graphs
European Journal of Combinatorics, 2010 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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Packing tight Hamilton cycles in 3-uniform hypergraphs [PDF]
, 2011 Let H be a 3-uniform hypergraph with N vertices. A tight Hamilton cycle C \subset H is a collection of N edges for which there is an ordering of the vertices v_1, ..., v_N such that every triple of consecutive vertices {v_i, v_{i+1}, v_{i+2}} is an edge ...
Alan Frieze +2 more
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The square of a Hamilton cycle in randomly perturbed graphs [PDF]
Random Struct. Algorithms, 2022 We investigate the appearance of the square of a Hamilton cycle in the model of randomly perturbed graphs, which is, for a given α∈(0,1)$$ \alpha \in \left(0,1\right) $$ , the union of any n$$ n $$ ‐vertex graph with minimum degree αn$$ \alpha n $$ and ...
Julia Böttcher +3 more
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Rainbow powers of a Hamilton cycle in Gn,p [PDF]
Journal of Graph Theory, 2022 We show that the threshold for having a rainbow copy of a power of a Hamilton cycle in a randomly edge colored copy of Gn,p ${G}_{n,p}$ is within a constant factor of the uncolored threshold.
Tolson Bell, A. Frieze
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Transversal Hamilton Cycle in Hypergraph Systems [PDF]
SIAM Journal on Discrete Mathematics, 2021 A $k$-graph system $\textbf{H}=\{H_i\}_{i\in[m]}$ is a family of not necessarily distinct $k$-graphs on the same $n$-vertex set $V$ and a $k$-graph $H$ on $V$ is said to be $\textbf{H}$-transversal provided that there exists an injection $\varphi: E(H ...
Yangyang Cheng +4 more
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A Hamilton Cycle in the k-Sided Pancake Network [PDF]
International Workshop on Combinatorial Algorithms, 2021 We present a Hamilton cycle in the $k$-sided pancake network and four combinatorial algorithms to traverse the cycle. The network's vertices are coloured permutations $\pi = p_1p_2\cdots p_n$, where each $p_i$ has an associated colour in $\{0,1,\ldots, k{
B. Cameron, J. Sawada, A. Williams
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Fast algorithms for solving the Hamilton Cycle problem with high probability [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2021 We study the Hamilton cycle problem with input a random graph G=G(n,p) in two settings. In the first one, G is given to us in the form of randomly ordered adjacency lists while in the second one we are given the adjacency matrix of G.
Michael Anastos
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On Hamilton cycle decompositions of
Discrete Mathematics, 2013 Michael W. Schroeder
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