Results 31 to 40 of about 445,337 (327)
Discrete Mathematics, 1993 If the complete graph on \(n\) vertices is edge-colored such that the number of times that a color may occur is less than \(cn/\log(n)\), where \(c\) is a fixed constant, then there is a Hamiltonian cycle in which no two edges have the same color.
Frieze, Alan, Reed, Bruce
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Hamilton cycles in hypergraphs below the Dirac threshold [PDF]
, 2018 We establish a precise characterisation of $4$-uniform hypergraphs with minimum codegree close to $n/2$ which contain a Hamilton $2$-cycle. As an immediate corollary we identify the exact Dirac threshold for Hamilton $2$-cycles in $4$-uniform hypergraphs.
Garbe, Frederik, Mycroft, Richard
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Hamilton-connected properties in cartesian product [PDF]
Transactions on Combinatorics, 2012 In this paper, we investigate a problem of finding natural condition to assure the product of two graphs to be hamilton-connected. We present some sufficient and necessary conditions for $GBox H$ being hamilton-connected when $G$ is a hamilton-connected ...
Rushengul Hoshur, Elkin Vumar
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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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Rainbow Hamilton Cycles in Uniform Hypergraphs [PDF]
The Electronic Journal of Combinatorics, 2012 Let $K_n^{(k)}$ be the complete $k$-uniform hypergraph, $k\ge3$, and let $\ell$ be an integer such that $1\le \ell\le k-1$ and $k-\ell$ divides $n$. An $\ell$-overlapping Hamilton cycle in $K_n^{(k)}$ is a spanning subhypergraph $C$ of $K_n^{(k)}$ with $n/(k-\ell)$ edges and such that for some cyclic ordering of the vertices each edge of $C$ consists
Dudek, Andrzej +2 more
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Edge condition for hamiltonicity in balanced tripartite graphs [PDF]
Opuscula Mathematica, 2009 A well-known theorem of Entringer and Schmeichel asserts that a balanced bipartite graph of order \(2n\) obtained from the complete balanced bipartite \(K_{n,n}\) by removing at most \(n-2\) edges, is bipancyclic.
Janusz Adamus
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Perfect Set of Euler Tours of Kp,p,p
Discussiones Mathematicae Graph Theory, 2016 Bermond conjectured that if G is Hamilton cycle decomposable, then L(G), the line graph of G, is Hamilton cycle decomposable. In this paper, we construct a perfect set of Euler tours for the complete tripartite graph Kp,p,p for any prime p and hence ...
Govindan T., Muthusamy A.
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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.
Frieze, Alan, Loh, Po-Shen
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Loose Hamilton Cycles in Regular Hypergraphs [PDF]
Combinatorics, Probability and Computing, 2014 We establish a relation between two uniform models of randomk-graphs (for constantk⩾ 3) onnlabelled vertices: ℍ(k)(n,m), the randomk-graph with exactlymedges, and ℍ(k)(n,d), the randomd-regulark-graph. By extending the switching technique of McKay and Wormald tok-graphs, we show that, for some range ofd = d(n)and a constantc> 0, ifm~cnd, then one ...
Dudek, Andrzej +3 more
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Electronic Journal of Graph Theory and Applications, 2021 A Hamiltonian graph G = (V,E) is called hyper-Hamiltonian if G-v is Hamiltonian for any v ∈ V(G). G is called a circulant if its automorphism group contains a |V(G)|-cycle.
Zbigniew R. Bogdanowicz
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