Results 1 to 10 of about 3,218,251 (319)
Resilience for loose Hamilton cycles [PDF]
Procedia Computer Science, 2023 We study the emergence of loose Hamilton cycles in subgraphs of random hypergraphs. Our main result states that the minimum $d$-degree threshold for loose Hamiltonicity relative to the random $k$-uniform hypergraph $H_k(n,p)$ coincides with its dense analogue whenever $p \geq n^{- (k-1)/2+o(1)}$.
Jos'e D. Alvarado +4 more
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Constructing Hamilton cycles and perfect matchings efficiently [PDF]
European Conference on Combinatorics, Graph Theory and Applications, 2022 Starting with the empty graph on $[n]$, at each round, a set of $K=K(n)$ edges is presented chosen uniformly at random from the ones that have not been presented yet.
Michael Anastos
semanticscholar +3 more sources
k-Ordered Hamilton cycles in digraphs [PDF]
Journal of Combinatorial Theory, Series B, 2007 Given a digraph D, the minimum semi-degree of D is the minimum of its minimum indegree and its minimum outdegree. D is k-ordered Hamiltonian if for every ordered sequence of k distinct vertices there is a directed Hamilton cycle which encounters these vertices in this order.
Daniela Kühn +2 more
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Counting Hamilton Cycles in Dirac Hypergraphs
Combinatorica, 2023 For $$0\le \ell 1 / 2 has (asymptotically and up to a subexponential factor) at least as many Hamilton $$\ell $$ ℓ -cycles as a typical random k -graph with edge-probability $$\delta $$ δ .
Asaf Ferber, Liam Hardiman, Adva Mond
semanticscholar +2 more sources
Perfect Matchings and Loose Hamilton Cycles in the Semirandom Hypergraph Model [PDF]
Random Struct. Algorithms, 2023 We study the 2‐offer semirandom 3‐uniform hypergraph model on n$$ n $$ vertices. At each step, we are presented with 2 uniformly random vertices. We choose any other vertex, thus creating a hyperedge of size 3.
Michael Molloy +2 more
semanticscholar +2 more sources
M-alternating Hamilton paths and M-alternating Hamilton cycles [PDF]
Discrete Mathematics, 2017 published in Discrete ...
Zan‐Bo Zhang, Yueping Li, Dingjun Lou
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Hamilton Cycles in Double Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2019 Coxeter referred to generalizing the Petersen graph. Zhou and Feng modified the graphs and introduced the double generalized Petersen graphs (DGPGs). Kutnar and Petecki proved that DGPGs are Hamiltonian in special cases and conjectured that all DGPGs are
Sakamoto Yutaro
doaj +2 more sources
Hamilton cycles in 3‐out [PDF]
Random Structures & Algorithms, 2009 AbstractLet G3‐out denote the random graph on vertex set [n] in which each vertex chooses three neighbors uniformly at random. Note that G3‐out has minimum degree 3 and average degree 6. We prove that the probability that G3‐out is Hamiltonian goes to 1 as n tends to infinity. © 2009 Wiley Periodicals, Inc. Random Struct.
Tom Bohman, Alan Frieze
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An O(n) time algorithm for finding Hamilton cycles with high probability [PDF]
Information Technology Convergence and Services, 2020 We design a randomized algorithm that finds a Hamilton cycle in $\mathcal{O}(n)$ time with high probability in a random graph $G_{n,p}$ with edge probability $p\ge C \log n / n$.
R. Nenadov, A. Steger, Pascal Su
semanticscholar +2 more sources
Colorful Hamilton cycles in random graphs
SIAM Journal on Discrete Mathematics, 2021 fixed minor ...
Debsoumya Chakraborti +2 more
openalex +4 more sources