Results 81 to 90 of about 78,303 (310)
Subgraphs intersecting any hamiltonian cycle
Journal of Combinatorial Theory, Series B, 1988 Let G be a subgraph of K(n), the complete graph on n vertices, such that (i) its edges cannot be represented by fewer than k vertices, (ii) every hamiltonian cycle of K(n) contains at least one edge of G and no proper subgraph of G has this property. P. Erdős posed the question of determining min e(G).
openaire +1 more source
Spin and Charge Control of Topological End States in Chiral Graphene Nanoribbons on a 2D Ferromagnet
Advanced Materials, EarlyView.Chiral graphene nanoribbons on a ferromagnetic gadolinium‐gold surface alloy display tunable spin and charge states at their termini. Atomic work function variations and exchange fields enabe transitions between singlet, doublet, and triplet configurations.
Leonard Edens +8 more
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Polynomial algorithms that prove an NP-hard hypothesis implies an NP-hard conclusion [PDF]
, 1999 A number of results in Hamiltonian graph theory are of the form $\mathcal{P}$$_{1}$ implies $\mathcal{P}$$_{2}$, where $\mathcal{P}$$_{1}$ is a property of graphs that is NP-hard and $\mathcal{P}$$_{2}$ is a cycle structure property of graphs that is ...
Bauer, D. +3 more
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Advanced Materials, EarlyView.Magnetic doping of the topological insulator Bi2Te3 with erbium adatoms induces out‐of‐plane magnetism and breaks time‐reversal symmetry, opening a Dirac gap and driving a Fermi surface transition from hexagonal to star‐of‐David geometry. Microscopy, spectroscopy, and magnetic dichroism reveal atomically controlled magnetic interactions that tailor the
Beatriz Muñiz Cano +18 more
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Local properties of graphs that induce global cycle properties [PDF]
Opuscula MathematicaA graph \(G\) is locally Hamiltonian if \(G[N(v)]\) is Hamiltonian for every vertex \(v\in V(G)\). In this note, we prove that every locally Hamiltonian graph with maximum degree at least \(|V(G)| - 7\) is weakly pancyclic.
Yanyan Wang, Xiaojing Yang
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2-Connected Hamiltonian Claw-Free Graphs Involving Degree Sum of Adjacent Vertices
Discussiones Mathematicae Graph Theory, 2020 For a graph H, define σ¯2(H)=min{d(u)+d(v)|uv∈E(H)}{{\bar \sigma }_2} ( H ) = \min \left\{ {d ( u ) + d ( v )|uv \in E ( H )} \right\} . Let H be a 2-connected claw-free simple graph of order n with δ(H) ≥ 3. In [J. Graph Theory 86 (2017) 193–212], Chen
Tian Tao, Xiong Liming
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Advanced Materials, EarlyView.A high‐capacity polyimide‐linked porous organic polymer (HAT‐PTO) incorporating numerous redox‐active centers is synthesized via a hydrothermal reaction, delivering a high theoretical capacity of 484 mAh g−1. In situ hybridization with carboxyl‐functionalized multiwalled carbon nanotubes enhances conductivity and stability, achieving 397 mAh g−1 at C ...
Arindam Mal +7 more
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Hamiltonian cycles in Cayley graphs of imprimitive complex reflection groups [PDF]
, 2014 Generalizing a result of Conway, Sloane, and Wilkes for real reflection groups, we show the Cayley graph of an imprimitive complex reflection group with respect to standard generating reflections has a Hamiltonian cycle.
Kriloff, Cathy, Lay, Terry
core
On the Hamiltonian Number of a Plane Graph
Discussiones Mathematicae Graph Theory, 2019 The Hamiltonian number of a connected graph is the minimum of the lengths of the closed spanning walks in the graph. In 1968, Grinberg published a necessary condition for the existence of a Hamiltonian cycle in a plane graph, formulated in terms of the ...
Lewis Thomas M.
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Discussiones Mathematicae Graph Theory, 2020 Let S = (a1,. . . , am; b1, . . . , bn), where a1, . . . , am and b1, . . . , bn are two sequences of nonnegative integers. We say that S is a bigraphic pair if there exists a simple bipartite graph G with partite sets {x1, x2, . . . , xm} and {y1, y2, .
Yin Jian-Hua, Li Sha-Sha
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