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Complexity of Hamiltonian Cycle Reconfiguration [PDF]
Algorithms, 2018 The Hamiltonian cycle reconfiguration problem asks, given two Hamiltonian cycles C 0 and C t of a graph G, whether there is a sequence of Hamiltonian cycles C 0 , C 1 , … , C t such that C i can be obtained ...
Asahi Takaoka
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Extending a perfect matching to a Hamiltonian cycle [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Graph ...
Adel Alahmadi +5 more
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Universally Hard Hamiltonian Cycle Problem Instances
International Joint Conference on Computational Intelligence, 2022 : In 2021, evolutionary algorithms found the hardest-known yes and no instances for the Hamiltonian cycle problem. These instances, which show regularity patterns, require a very high number of recursions for the best exact backtracking algorithm ...
Joeri Sleegers +2 more
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Enumeration of Hamiltonian Cycles on a Thick Grid Cylinder -- Part II:\n Contractible Hamiltonian Cycles [PDF]
Applicable Analysis and Discrete Mathematics, 2021 In a recent paper, we have studied the enumeration of Hamiltonian cycles (abbreviated HCs) on the grid cylinder graph Pm+1 x Cn, where m grows while n is fixed. In this sequel, we study a much harder problem of enumerating HCs on the same graph only this time letting n grow while m is fixed.
Olga Bodroža-Pantić +4 more
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Hamiltonian cycles in torical lattices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 We establish sufficient conditions for a toric lattice $T_{m,n}$ to be Hamiltonian. Also, we give some asymptotics for the number of Hamiltonian cycles in $T_{m,n}$.
Vladimir K. Leontiev
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On Vertices Enforcing a Hamiltonian Cycle
Discussiones Mathematicae Graph Theory, 2013 A nonempty vertex set X ⊆ V (G) of a hamiltonian graph G is called an H-force set of G if every X-cycle of G (i.e. a cycle of G containing all vertices of X) is hamiltonian.
Fabrici Igor +2 more
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Symmetry classes of Hamiltonian cycles [PDF]
27 pages, 13 ...
Julia Baligacs +3 more
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On pre-Hamiltonian Cycles in Hamiltonian Digraphs [PDF]
, 2014 Let $D$ be a strongly connected directed graph of order $n\geq 4$. In \cite{[14]} (J. of Graph Theory, Vol.16, No. 5, 51-59, 1992) Y. Manoussakis proved the following theorem: Suppose that $D$ satisfies the following condition for every triple $x,y,z$ of vertices such that $x$ and $y$ are non-adjacent: If there is no arc from $x$ to $z$, then $d(x)+d(y)
Samvel Kh. Darbinyan
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Ore-degree threshold for the square of a Hamiltonian cycle [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Graph ...
Louis DeBiasio +2 more
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On $2$-pyramidal Hamiltonian cycle systems [PDF]
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2014 Let \(\hat K_{2n}\) denote the complete graph \(K_{2n}\) with the edges in a perfect matching removed and let \(\hat K_{2n+1} = K_{2n+1}\). A Hamiltonian cycle system (HCS) of order \(v\) is a decomposition of the edge set of \(\hat K_v\) into a disjoint union of Hamiltonian cycles. Such a system \(H\) is called 1-rotational (resp.
R. A. Bailey +3 more
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