Results 11 to 20 of about 43 (43)
Decomposing tournaments into paths
Proceedings of the London Mathematical Society, Volume 121, Issue 2, Page 426-461, August 2020., 2020 Abstract We consider a generalisation of Kelly's conjecture which is due to Alspach, Mason, and Pullman from 1976. Kelly's conjecture states that every regular tournament has an edge decomposition into Hamilton cycles, and this was proved by Kühn and Osthus for large tournaments. The conjecture of Alspach, Mason, and Pullman asks for the minimum number
Allan Lo +3 more
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Hamiltonian paths on Platonic graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 30, Page 1613-1616, 2004., 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 topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph
Brian Hopkins
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Old and new generalizations of line graphs
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 29, Page 1509-1521, 2004., 2004 Line graphs have been studied for over seventy years. In 1932, H. Whitney showed that for connected graphs, edge‐isomorphism implies isomorphism except for K3 and K1,3. The line graph transformation is one of the most widely studied of all graph transformations.
Jay Bagga
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Lower Bound on the Number of Hamiltonian Cycles of Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2020 In this paper, we investigate the number of Hamiltonian cycles of a generalized Petersen graph P (N, k) and prove that Ψ(P(N,3))⩾N⋅αN,\Psi ( {P ( {N,3} )} ) \ge N \cdot {\alpha _N}, where Ψ(P(N, 3)) is the number of Hamiltonian cycles of P(N, 3) and αN ...
Lu Weihua, Yang Chao, Ren Han
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Longest cycles in certain bipartite graphs
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 103-106, 1998., 1995 Let G be a connected bipartite graph with bipartition (X, Y) such that |X| ≥ |Y|(≥2), n = |X| and m = |Y|. Suppose, for all vertices x ∈ X and y ∈ Y, dist(x, y) = 3 implies d(x) + d(y) ≥ n + 1. Then G contains a cycle of length 2m. In particular, if m = n, then G is hamiltomian.
Pak-Ken Wong
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Hamiltonian‐connected graphs and their strong closures
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 745-747, 1997., 1993 Let G be a simple graph of order at least three. We show that G is Hamiltonian‐connected if and only if its strong closure is Hamiltonian‐connected. We also give an efficient algorithm to compute the strong closure of G.
Pak-Ken Wong
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Hamiltonicities of Double Domination Critical and Stable Claw-Free Graphs
Discussiones Mathematicae Graph Theory, 2019 A graph G with the double domination number γ×2(G) = k is said to be k- γ×2-critical if γ×2 (G + uv) < k for any uv ∉ E(G). On the other hand, a graph G with γ×2 (G) = k is said to be k-γ×2+$k - \gamma _{ \times 2}^ + $-stable if γ×2 (G + uv) = k for any
Kaemawichanurat Pawaton
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Notes on sufficient conditions for a graph to be Hamiltonian
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 4, Page 825-827, 1991., 1990 The first part of this paper deals with an extension of Dirac′s Theorem to directed graphs. It is related to a result often referred to as the Ghouila‐Houri Theorem. Here we show that the requirement of being strongly connected in the hypothesis of the Ghouila‐Houri Theorem is redundant. The Second part of the paper shows that a condition on the number
Michael Joseph Paul +2 more
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Hamiltonian and Pancyclic Graphs in the Class of Self-Centered Graphs with Radius Two
Discussiones Mathematicae Graph Theory, 2018 The paper deals with Hamiltonian and pancyclic graphs in the class of all self-centered graphs of radius 2. For both of the two considered classes of graphs we have done the following. For a given number n of vertices, we have found an upper bound of the
Hrnčiar Pavel, Monoszová Gabriela
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Hamilton Cycles in Double Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2019 Coxeter referred to generalizing the Petersen graph. Zhou and Feng modified the graphs and introduced the double generalized Petersen graphs (DGPGs). Kutnar and Petecki proved that DGPGs are Hamiltonian in special cases and conjectured that all DGPGs are
Sakamoto Yutaro
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