Results 1 to 10 of about 4,036,327 (265)
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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Hamiltonicity of 3tEC Graphs with α=κ+1
Journal of Mathematics, 2021 A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γtG of G.
Huanying He, Xinhui An, Zongjun Zhao
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Hamilton cycles in sparse robustly expanding digraphs [PDF]
, 2018 The notion of robust expansion has played a central role in the solution of several conjectures involving the packing of Hamilton cycles in graphs and directed graphs.
Lo, Allan, Patel, Viresh
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Discrete Mathematics, 2010 In this paper, it is shown that the tensor product of the complete bipartite graph, K"r","r,r>=2, and the regular complete multipartite graph, K"m*[email protected]?"n,m>=3, is Hamilton cycle decomposable.
R. Manikandan, P. Paulraja
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Hamilton cycles in graphs and hypergraphs: an extremal perspective [PDF]
, 2014 As one of the most fundamental and well-known NP-complete problems, the Hamilton cycle problem has been the subject of intensive research. Recent developments in the area have highlighted the crucial role played by the notions of expansion and quasi ...
Kühn, Daniela, Osthus, Deryk
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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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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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An update on the middle levels problem
, 2006 The middle levels problem is to find a Hamilton cycle in the middle levels, M_{2k+1}, of the Hasse diagram of B_{2k+1} (the partially ordered set of subsets of a 2k+1-element set ordered by inclusion).
Savage, Carla D. +2 more
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Enumerating all Hamilton Cycles and Bounding the Number of Hamilton Cycles in 3-Regular Graphs [PDF]
The Electronic Journal of Combinatorics, 2011 We describe an algorithm which enumerates all Hamilton cycles of a given 3-regular $n$-vertex graph in time $O(1.276^{n})$, improving on Eppstein's previous bound. The resulting new upper bound of $O(1.276^{n})$ for the maximum number of Hamilton cycles in 3-regular $n$-vertex graphs gets close to the best known lower bound of $\Omega(1.259^{n})$.
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System dynamics simulation of the thermal dynamic processes in nuclear power plants
Nuclear Engineering and Technology, 2019 A nuclear power plant (NPP) is a highly complex system-of-systems as manifested through its internal systems interdependence. The negative impact of such interdependence was demonstrated through the 2011 Fukushima Daiichi nuclear disaster. As such, there
Mohamed El-Sefy +4 more
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