Results 31 to 40 of about 43 (43)
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 Note on Cycles in Locally Hamiltonian and Locally Hamilton-Connected Graphs
Discussiones Mathematicae Graph Theory, 2020 Let 𝒫 be a property of a graph. A graph G is said to be locally 𝒫, if the subgraph induced by the open neighbourhood of every vertex in G has property 𝒫. Ryjáček conjectures that every connected, locally connected graph is weakly pancyclic.
Tang Long, Vumar Elkin
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Matchings of quadratic size extend to long cycles in hypercubes [PDF]
Discrete Mathematics & Theoretical Computer Science, 2016 Ruskey and Savage in 1993 asked whether every matching in a hypercube can be extended to a Hamiltonian cycle. A positive answer is known for perfect matchings, but the general case has been resolved only for matchings of linear size.
Tomáš Dvořák
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2-Spanning Cyclability Problems of Some Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2020 A graph G is called r-spanning cyclable if for every r distinct vertices v1, v2, . . . , vr of G, there exists r cycles C1, C2, . . . , Cr in G such that vi is on Ci for every i, and every vertex of G is on exactly one cycle Ci.
Yang Meng-Chien +3 more
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Spectral Radius and Hamiltonicity of Graphs
Discussiones Mathematicae Graph Theory, 2019 In this paper, we study the Hamiltonicity of graphs with large minimum degree. Firstly, we present some conditions for a simple graph to be Hamilton-connected and traceable from every vertex in terms of the spectral radius of the graph or its complement,
Yu Guidong +3 more
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Forbidden Pairs and (k,m)-Pancyclicity
Discussiones Mathematicae Graph Theory, 2017 A graph G on n vertices is said to be (k, m)-pancyclic if every set of k vertices in G is contained in a cycle of length r for each r ∈ {m, m+1, . . . , n}.
Crane Charles Brian
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Variantes del problema del cartero mixto que se pueden resolver usando programación lineal
Revista de Matemática: Teoría y Aplicaciones, 2012 Dada una gráfica mixta y conexa con costos en sus aristas y arcos, el problema del cartero mixto consiste en encontrar un circuito cerrado de la gráfica mixta que recorra sus aristas y arcos a costo mínimo. Se sabe que este problema es NP-duro.
Francisco Javier Zaragoza Martínez +1 more
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Eulerian $k$-dominating reconfiguration graphs [PDF]
Discrete Mathematics & Theoretical Computer ScienceFor a graph $G$, the vertices of the $k$-dominating graph, denoted $\mathcal{D}_k(G)$, correspond to the dominating sets of $G$ with cardinality at most $k$. Two vertices of $\mathcal{D}_k(G)$ are adjacent if and only if the corresponding dominating sets
M. E. Messinger, A. Porter
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Heavy Subgraphs, Stability and Hamiltonicity
Discussiones Mathematicae Graph Theory, 2017 Let G be a graph. Adopting the terminology of Broersma et al. and Čada, respectively, we say that G is 2-heavy if every induced claw (K1,3) of G contains two end-vertices each one has degree at least |V (G)|/2; and G is o-heavy if every induced claw of G
Li Binlong, Ning Bo
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ALTERNATING AND SYMMETRIC GROUPS WITH EULERIAN GENERATING GRAPH
Forum of Mathematics, Sigma, 2017 Given a finite group $G$ , the generating graph $\unicode[STIX]{x1D6E4}(G)$
ANDREA LUCCHINI, CLAUDE MARION
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