Results 41 to 50 of about 3,218,251 (319)
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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A Note Concerning Hamilton Cycles in Some Classes of Grid Graphs
Journal of Mathematical and Fundamental Sciences, 2013 A graph G is called hamiltonian if it contains a Hamilton cycle, i.e. a cycle containing all vertices. Deciding whether a given graph has a Hamilton cycle is an NP-complete problem. But, it is a polynomial problem within some special graph classes.
A. N.M. Salman +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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Two Sufficient Conditions for Hamilton and Dominating Cycles
International Journal of Mathematics and Mathematical Sciences, 2012 We prove that if is a 2-connect graph of size (the number of edges) and minimum degree with , where when and when , then each longest cycle in is a dominating cycle.
Zh. G. Nikoghosyan
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Testing of pandemic ventilators under early and agile development
Frontiers in Medical Technology, 2022 Aiming to address clinical requirements subsequent to SARS-CoV-2-related pulmonary disease, multiple research groups and industry groups carried out intensive studies to develop pandemic ventilators (PDVs).
Nikolaos Tachatos +7 more
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Graph Invariants and Large Cycles: A Survey
International Journal of Mathematics and Mathematical Sciences, 2011 Graph invariants provide a powerful analytical tool for investigation of abstract substructures of graphs. This paper is devoted to large cycle substructures, namely, Hamilton, longest and dominating cycles and some generalized cycles including Hamilton ...
Zh. G. Nikoghosyan
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Counting Hamilton cycles in Dirac hypergraphs [PDF]
Combinatorics, probability & computing, 2019 A tight Hamilton cycle in a k-uniform hypergraph (k-graph) G is a cyclic ordering of the vertices of G such that every set of k consecutive vertices in the ordering forms an edge.
Stefan Glock +4 more
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A short proof of the middle levels theorem
Discrete Analysis, 2018 A short proof of the middle-levels theorem, Discrete Analysis 2018:8, 12 pp. Let $n$ be a positive integer, and define a bipartite graph where one vertex set consists of all subsets of $\{1,2,\dots,2n+1\}$ of size $n$, the other consists of all subsets ...
Petr Gregor +2 more
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Hamilton cycles in random graphs with minimum degree at least 3: An improved analysis [PDF]
Random Struct. Algorithms, 2019 In this paper we consider the existence of Hamilton cycles in the random graph G=Gn,mδ≥3 . This random graph is chosen uniformly from 𝒢n,mδ≥3 , the set of graphs with vertex set [n], m edges and minimum degree at least 3.
Michael Anastos, A. Frieze
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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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