Results 11 to 20 of about 4,036,327 (265)
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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Symmetric Hamilton Cycle Decompositions of Complete Multigraphs
Discussiones Mathematicae Graph Theory, 2013 Let n ≥ 3 and ⋋ ≥ 1 be integers. Let ⋋Kn denote the complete multigraph with edge-multiplicity ⋋. In this paper, we show that there exists a symmetric Hamilton cycle decomposition of ⋋K2m for all even ⋋ ≥ 2 and m ≥ 2.
Chitra V., Muthusamy A.
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Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords
Discussiones Mathematicae Graph Theory, 2015 It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required.
Affif Chaouche Fatima +2 more
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Hamilton cycles in quasirandom hypergraphs [PDF]
Random Structures & Algorithms, 2015 We show that, for a natural notion of quasirandomness in $k$-uniform hypergraphs, any quasirandom $k$-uniform hypergraph on $n$ vertices with constant edge density and minimum vertex degree $\Omega(n^{k-1})$ contains a loose Hamilton cycle.
Lenz, John +2 more
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Fast strategies in biased Maker--Breaker games [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 We study the biased $(1:b)$ Maker--Breaker positional games, played on the edge set of the complete graph on $n$ vertices, $K_n$. Given Breaker's bias $b$, possibly depending on $n$, we determine the bounds for the minimal number of moves, depending on ...
Mirjana Mikalački, Miloš Stojaković
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Loose Hamilton cycles in hypergraphs
Discrete Mathematics, 2011 We prove that any k-uniform hypergraph on n vertices with minimum degree at least n/(2(k-1))+o(n) contains a loose Hamilton cycle. The proof strategy is similar to that used by K hn and Osthus for the 3-uniform case. Though some additional difficulties arise in the k-uniform case, our argument here is considerably simplified by applying the recent ...
Keevash, Peter +3 more
openaire +4 more sources
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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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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The threshold for the square of a Hamilton cycle [PDF]
Proceedings of the American Mathematical Society, 2020 Resolving a conjecture of Kühn and Osthus from 2012, we show that p = 1 / n p= 1/\sqrt {n} is the threshold for the random graph G n
J. Kahn +2 more
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Symmetric Hamilton cycle decompositions of complete graphs minus a 1‐factor
Journal of Combinatorial Designs, 2011 R. Brualdi, Michael W. Schroeder
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