Results 21 to 30 of about 384 (59)
Discussiones Mathematicae Graph Theory, 2022 A graph is called Hamiltonian extendable if there exists a Hamiltonian path between any two nonadjacent vertices. In this paper, we give an explicit formula of the minimum number of edges for Hamiltonian extendable graphs and we also characterize the ...
Yang Xiaojing, Xiong Liming
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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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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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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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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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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 sharp lower bound on the signless Laplacian index of graphs with (κ,τ)-regular sets
Special Matrices, 2018 A new lower bound on the largest eigenvalue of the signless Laplacian spectra for graphs with at least one (κ,τ)regular set is introduced and applied to the recognition of non-Hamiltonian graphs or graphs without a perfect matching.
Andeelić Milica +2 more
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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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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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Notes on a conjecture of Manoussakis concerning Hamilton cycles in digraphs
, 2014 In 1992, Manoussakis conjectured that a strongly 2-connected digraph $D$ on $n$ vertices is hamiltonian if for every two distinct pairs of independent vertices $x,y$ and $w,z$ we have $d(x)+d(y)+d(w)+d(z)\geq 4n-3$.
Ning, Bo
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