Results 21 to 30 of about 77,685 (270)
A remark on Hamiltonian cycles
Journal of Combinatorial Theory, Series B, 1981 AbstractEvery 2-connected graph G with δ ⩾ (v + κ)3 is hamiltonian where v denotes the order, δ the minimum degree and κ the point connectivity of G.
Roland Häggkvist, G. G. Nicoghossian
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Grafos hamiltonianos en el diseño de viajes
Modelling in Science Education and Learning, 2013 The existence and, if applicable, the location of paths with given properties is a topic in graph theory. One of these problems is to find routes through all points, only once, starting and ending at the same node.
Cristina Jordán Lluch +1 more
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The H-force sets of the graphs satisfying the condition of Ore’s theorem
Open Mathematics, 2020 Let G be a Hamiltonian graph. A nonempty vertex set X⊆V(G)X\subseteq V(G) is called a Hamiltonian cycle enforcing set (in short, an H-force set) of G if every X-cycle of G (i.e., a cycle of G containing all vertices of X) is a Hamiltonian cycle.
Zhang Xinhong, Li Ruijuan
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Matchings Extend to Hamiltonian Cycles in 5-Cube
Discussiones Mathematicae Graph Theory, 2018 Ruskey and Savage asked the following question: Does every matching in a hypercube Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? Fink confirmed that every perfect matching can be extended to a Hamiltonian cycle of Qn, thus solved Kreweras’ conjecture.
Wang Fan, Zhao Weisheng
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A result on Hamiltonian line graphs involving restrictions on induced subgraphs [PDF]
, 1988 It is shown that the existence of a Hamilton cycle in the line graph of a graph G can be ensured by imposing certain restrictions on certain induced subgraphs of G.
Benhocine +11 more
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Graphs with few hamiltonian cycles
Mathematics of Computation, 2019 We describe an algorithm for the exhaustive generation of non-isomorphic graphs with a given number k ≥
Goedgebeur, Jan +2 more
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Orientations of hamiltonian cycles in large digraphs [PDF]
, 1986 We prove that, with some exceptions, every digraph with n ≥ 9 vertices and at least (n - 1) (n - 2) + 2 arcs contains all orientations of a Hamiltonian ...
Adam Pawel Wojda +3 more
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The parity Hamiltonian cycle problem
Discrete Mathematics, 2018 Motivated by a relaxed notion of the celebrated Hamiltonian cycle, this paper investigates its variant, parity Hamiltonian cycle (PHC): A PHC of a graph is a closed walk which visits every vertex an odd number of times, where we remark that the walk may use an edge more than once. First, we give a complete characterization of the graphs which have PHCs,
Hiroshi Nishiyama +4 more
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Alternating Hamiltonian cycles in $2$-edge-colored multigraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2019 A path (cycle) in a $2$-edge-colored multigraph is alternating if no two consecutive edges have the same color. The problem of determining the existence of alternating Hamiltonian paths and cycles in $2$-edge-colored multigraphs is an $\mathcal{NP ...
Alejandro Contreras-Balbuena +2 more
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Hamiltonian Chains in Hypergraphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Hamiltionian chain is a generalisation of hamiltonian cycles for hypergraphs. Among the several possible ways of generalisations this is probably the most strong one, it requires the strongest structure.
Gyula Y. Katona
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