Results 41 to 50 of about 78,303 (310)
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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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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Removable matchings and hamiltonian cycles
Discrete Mathematics, 2009 The authors show the following two results: {\parindent=5mm \begin{itemize}\item[1)]Let \(G\) be a graph of order \(n\geq 4k+3\) with \(\sigma_2 (G)\geq n\) and let \(F\) be a matching of size \(k\) in \(G\) such that \(G-F\) is 2-connected. Then \(G-F\) is hamiltonian or \(G\cong K_2 +(K_2\cup K_{n-4})\) or \(G\cong \bar{K_2} +(K_2\cup K_{n-4 ...
Hu, Zhiquan, Li, Hao
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Hierarchical Hexagon: A New Fault-Tolerant Interconnection Network for Parallel Systems
Cybernetics and Information Technologies, 2021 A new interconnection network topology called Hierarchical Hexagon HH(n) is proposed for massively parallel systems. The new network uses a hexagon as the primary building block and grows hierarchically.
Tripathy Laxminath +1 more
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Hamiltonian paths on Platonic graphs
International Journal of Mathematics and Mathematical Sciences, 2004 We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate
Brian Hopkins
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Energy Conditions for Hamiltonian and Traceable Graphs
Universal Journal of Mathematics and Applications, 2019 A graph is called Hamiltonian (resp. traceable) if the graph has a Hamiltonian cycle (resp. path), a cycle (resp. path) containing all the vertices of the graph. The energy of a graph is defined as the sum of the absolute values of the eigenvalues of the
Rao Li
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Advanced Functional Materials, Volume 35, Issue 12, March 18, 2025.In this study, the unique role of the unusual lone‐pair‐π conjugation mechanism in poly(1,4‐anthraquinone) (P14AQ) is explored as an organic electrode material. Unlike traditional π‐π interactions, P14AQ's conjugation involves lone pairs of oxygen atoms interacting with the π cloud of adjacent units, enabling stable charge transport even with minimal π‐
Xiaotong Zhang, Piotr de Silva
wiley +1 more source
Hamiltonian chordal graphs are not cycle extendible [PDF]
, 2014 In 1990, Hendry conjectured that every Hamiltonian chordal graph is cycle extendible; that is, the vertices of any non-Hamiltonian cycle are contained in a cycle of length one greater.
Lafond, Manuel, Seamone, Ben
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