Results 21 to 30 of about 1,699 (154)
Pancyclicity and vertex pancyclicity for some products of graphs
, 2023 Artchariya Muaengwaeng
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The vertex-pancyclicity of the simplified shuffle-cube and the vertex-bipancyclicity of the balanced shuffle-cube [PDF]
International Journal of Computer Mathematics Computer Systems TheoryA graph $G$ $=$ $(V,E)$ is vertex-pancyclic if for every vertex $u$ and any integer $l$ ranging from $3$ to $|V|$, $G$ contains a cycle $C$ of length $l$ such that $u$ is on $C$. A bipartite graph $G$ $=$ $(V,E)$ is vertex-bipancyclic if for every vertex
Yasong Liu, Huazhong Lü
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Forbidden subgraphs for chorded pancyclicity [PDF]
Discrete Mathematics, 2017 We call a graph $G$ pancyclic if it contains at least one cycle of every possible length $m$, for $3\le m\le |V(G)|$. In this paper, we define a new property called chorded pancyclicity. We explore forbidden subgraphs in claw-free graphs sufficient to imply that the graph contains at least one chorded cycle of every possible length $4, 5, \ldots, |V(G)|
Megan Cream +2 more
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Pancyclicity of randomly perturbed digraph
JUSTC, 2022 Dirac’s theorem states that if a graph G on n vertices has a minimum degree of at least \begin{document}$\displaystyle \frac{n}{2}$\end{document}, then G contains a Hamiltonian cycle. Bohman et al.
Zelin Ren, Xinmin Hou
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Hamiltonicity of graphs perturbed by a random regular graph
Random Structures &Algorithms, Volume 62, Issue 4, Page 857-886, July 2023., 2023 Abstract We study Hamiltonicity and pancyclicity in the graph obtained as the union of a deterministic n$$ n $$‐vertex graph H$$ H $$ with δ(H)≥αn$$ \delta (H)\ge \alpha n $$ and a random d$$ d $$‐regular graph G$$ G $$, for d∈{1,2}$$ d\in \left\{1,2\right\} $$. When G$$ G $$ is a random 2‐regular graph, we prove that a.a.s.
Alberto Espuny Díaz, António Girão
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Hamiltonicity of graphs perturbed by a random geometric graph
Journal of Graph Theory, Volume 103, Issue 1, Page 12-22, May 2023., 2023 Abstract We study Hamiltonicity in graphs obtained as the union of a deterministic n $n$‐vertex graph H $H$ with linear degrees and a d $d$‐dimensional random geometric graph G d ( n , r ) ${G}^{d}(n,r)$, for any d ≥ 1 $d\ge 1$. We obtain an asymptotically optimal bound on the minimum r $r$ for which a.a.s.
Alberto Espuny Díaz
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Hamilton‐Connected Mycielski Graphs∗
Discrete Dynamics in Nature and Society, Volume 2021, Issue 1, 2021., 2021 Jarnicki, Myrvold, Saltzman, and Wagon conjectured that if G is Hamilton‐connected and not K2, then its Mycielski graph μ(G) is Hamilton‐connected. In this paper, we confirm that the conjecture is true for three families of graphs: the graphs G with δ(G) > |V(G)|/2, generalized Petersen graphs GP(n, 2) and GP(n, 3), and the cubes G3.
Yuanyuan Shen +3 more
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Spectral Sufficient Conditions on Pancyclic Graphs
Complexity, Volume 2021, Issue 1, 2021., 2021 A pancyclic graph of order n is a graph with cycles of all possible lengths from 3 to n. In fact, it is NP‐complete that deciding whether a graph is pancyclic. Because the spectrum of graphs is convenient to be calculated, in this study, we try to use the spectral theory of graphs to study this problem and give some sufficient conditions for a graph to
Guidong Yu +4 more
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Computing Edge Weights of Symmetric Classes of Networks
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 Accessibility, robustness, and connectivity are the salient structural properties of networks. The labelling of networks with numeric numbers using the parameters of edge or vertex weights plays an eminent role in the study of the aforesaid properties.
Hafiz Usman Afzal +4 more
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