Results 31 to 40 of about 77,334 (248)
Problems on Shortest k-Node Cycles and Paths
Кібернетика та комп'ютерні технології, 2021 The paper is devoted to the construction of mathematical models for problems on the shortest cycles and paths, that pass through a given number of nodes of a directed graph.
Petro Stetsyuk +2 more
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Hamiltonian cycles in k‐partite graphs [PDF]
Journal of Graph Theory, 2019 AbstractChen et al determined the minimum degree threshold for which a balanced ‐partite graph has a Hamiltonian cycle. We give an asymptotically tight minimum degree condition for Hamiltonian cycles in arbitrary ‐partite graphs in that all parts have at most vertices (a necessary condition).
Louis DeBiasio +3 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 Extremal Hypergraphs for Hamiltonian Cycles [PDF]
Electronic Notes in Discrete Mathematics, 2011 We study sufficient conditions for Hamiltonian cycles in hypergraphs, and obtain both Tur n- and Dirac-type results. While the Tur n-type result gives an exact threshold for the appearance of a Hamiltonian cycle in a hypergraph depending only on the extremal number of a certain path, the Dirac-type result yields a sufficient condition relying solely ...
Glebov, Roman, Person, Yury, Weps, Wilma
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Decomposing the Complete Graph Into Hamiltonian Paths (Cycles) and 3-Stars
Discussiones Mathematicae Graph Theory, 2020 Let H be a graph. A decomposition of H is a set of edge-disjoint subgraphs of H whose union is H. A Hamiltonian path (respectively, cycle) of H is a path (respectively, cycle) that contains every vertex of H exactly once.
Lee Hung-Chih, Chen Zhen-Chun
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Hamiltonian Normal Cayley Graphs
Discussiones Mathematicae Graph Theory, 2019 A variant of the Lovász Conjecture on hamiltonian paths states that every finite connected Cayley graph contains a hamiltonian cycle. Given a finite group G and a connection set S, the Cayley graph Cay(G, S) will be called normal if for every g ∈ G we ...
Montellano-Ballesteros Juan José +1 more
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Enforced hamiltonian cycles in generalized dodecahedra
Electronic Journal of Graph Theory and Applications, 2013 The H-force number of a hamiltonian graph G is the smallest number k with the property that there exists a set W ⊆ V (G) with |W| = k such that each cycle passing through all vertices of W is a hamiltonian cycle.
Maria Timkova
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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,
Nishiyama, Hiroshi +4 more
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CONTRACTIBLE HAMILTONIAN CYCLES IN POLYHEDRAL MAPS [PDF]
Discrete Mathematics, Algorithms and Applications, 2012 We present a necessary and sufficient condition for existence of a contractible Hamiltonian cycle in the edge graph of equivelar maps on surfaces. We also present an algorithm to find such cycles (if they exist). This is further generalized and shown to hold for more general maps.
Maity, Dipendu, Upadhyay, Ashish Kumar
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On the H-Force Number of Hamiltonian Graphs and Cycle Extendability
Discussiones Mathematicae Graph Theory, 2017 The H-force number h(G) of a hamiltonian graph G is the smallest cardinality of a set A ⊆ V (G) such that each cycle containing all vertices of A is hamiltonian. In this paper a lower and an upper bound of h(G) is given.
Hexel Erhard
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