Results 41 to 50 of about 1,699 (154)
Tight Hamilton Cycles in Random Uniform Hypergraphs [PDF]
, 2010 In this paper we show that $e/n$ is the sharp threshold for the existence of tight Hamilton cycles in random $k$-uniform hypergraphs, for all $k\ge 4$. When $k=3$ we show that $1/n$ is an asymptotic threshold.
Dudek, Andrzej, Frieze, Alan
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Journal of Combinatorial Theory, Series B, 1976 Abstract A graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of all lengths l, 3 ≤ l ≤ | V(G) |. Theorem . Let G be Hamiltonian and suppose that |E(G)| ≥ n 2 4 , where n = |V(G)|. Then G is either pancyclic or else is the complete bipartite graph K n 2 , n 2 .
Bondy, J.A, Ingleton, A.W
openaire +2 more sources
A Note on Cycles in Locally Hamiltonian and Locally Hamilton-Connected Graphs
Discussiones Mathematicae Graph Theory, 2020 Let 𝒫 be a property of a graph. A graph G is said to be locally 𝒫, if the subgraph induced by the open neighbourhood of every vertex in G has property 𝒫. Ryjáček conjectures that every connected, locally connected graph is weakly pancyclic.
Tang Long, Vumar Elkin
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A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs
Discussiones Mathematicae Graph Theory, 2017 A graph G on n vertices is said to be pancyclic if it contains cycles of all lengths k for k ∈ {3, . . . , n}. A vertex v ∈ V (G) is called super-heavy if the number of its neighbours in G is at least (n+1)/2.
Wide Wojciech
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Pancyclicity of the n-Generalized Prism over Skirted Graphs
Symmetry, 2022 A side skirt is a planar rooted tree T, T≠P2, where the root of T is a vertex of degree at least two, and all other vertices except the leaves are of degree at least three.
Artchariya Muaengwaeng +2 more
semanticscholar +1 more source
Pancyclicity When Each Cycle Contains k Chords
Discussiones Mathematicae Graph Theory, 2019 For integers n ≥ k ≥ 2, let c(n, k) be the minimum number of chords that must be added to a cycle of length n so that the resulting graph has the property that for every l ∈ {k, k + 1, . . .
Taranchuk Vladislav
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Local properties of graphs that induce global cycle properties [PDF]
Opuscula MathematicaA graph \(G\) is locally Hamiltonian if \(G[N(v)]\) is Hamiltonian for every vertex \(v\in V(G)\). In this note, we prove that every locally Hamiltonian graph with maximum degree at least \(|V(G)| - 7\) is weakly pancyclic.
Yanyan Wang, Xiaojing Yang
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Proof of a conjecture of Thomassen on Hamilton cycles in highly connected tournaments
Proceedings of the London Mathematical Society, Volume 109, Issue 3, Page 733-762, September 2014., 2014 A conjecture of Thomassen from 1982 states that, for every k, there is an f(k) so that every strongly f(k)‐connected tournament contains k edge‐disjoint Hamilton cycles. A classical theorem of Camion, that every strongly connected tournament contains a Hamilton cycle, implies that f(1)=1. So far, even the existence of f(2) was open.
Daniela Kühn +3 more
wiley +1 more source
Notes on a conjecture of Manoussakis concerning Hamilton cycles in digraphs
, 2014 In 1992, Manoussakis conjectured that a strongly 2-connected digraph $D$ on $n$ vertices is hamiltonian if for every two distinct pairs of independent vertices $x,y$ and $w,z$ we have $d(x)+d(y)+d(w)+d(z)\geq 4n-3$.
Ning, Bo
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New Sufficient Conditions for Hamiltonian Paths
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.
M. Sohel Rahman +3 more
wiley +1 more source