Results 11 to 20 of about 105 (94)
Discussiones Mathematicae Graph Theory, 2015 For integers k and n with 2 ≤ k ≤ n − 1, a graph G of order n is k-path pancyclic if every path P of order k in G lies on a cycle of every length from k + 1 to n. Thus a 2-path pancyclic graph is edge-pancyclic.
Bi Zhenming, Zhang Ping
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Graphs which have pancyclic complements
International Journal of Mathematics and Mathematical Sciences, 1978 Let p and q denote the number of vertices and edges of a graph G, respectively. Let Δ(G) denote the maximum degree of G, and G¯ the complement of G. A graph G of order p is said to be pancyclic if G contains a cycle of each length n, 3≤n≤p.
H. Joseph Straight
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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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New sufficient conditions for Hamiltonian paths. [PDF]
ScientificWorldJournal, 2014 A Hamiltonian path in a graph is a path involving all the vertices of the graph. In this paper, we revisit the famous Hamiltonian path problem and present new sufficient conditions for the existence of a Hamiltonian path in a graph.
Rahman MS, Kaykobad M, Firoz JS.
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Chorded k-pancyclic and weakly k-pancyclic graphs
Discussiones Mathematicae Graph TheorySummary: As natural relaxations of pancyclic graphs, we say a graph \(G\) is \(k\)-pancyclic if \(G\) contains cycles of each length from \(k\) to \(|V(G)|\) and \(G\) is weakly pancyclic if it contains cycles of all lengths from the girth to the circumference of \(G\), while \(G\) is weakly \(k\)-pancyclic if it contains cycles of all lengths from \(k\
Megan Cream, Ronald J. Gould
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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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Rainbow Pancyclicity in Graph Systems [PDF]
The Electronic Journal of Combinatorics, 2021 Let $G_1,\ldots,G_n$ be graphs on the same vertex set of size $n$, each graph with minimum degree $\delta(G_i)\ge n/2$. A recent conjecture of Aharoni asserts that there exists a rainbow Hamiltonian cycle i.e. a cycle with edge set $\{e_1,\ldots,e_n\}$ such that $e_i\in E(G_i)$ for $1\leq i \leq n$.
Cheng, Yangyang +2 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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PANCYCLICITY IN LINE GRAPHS [PDF]
Acta Mathematica Scientia, 1998 For a graph \(G\), let \(\overline {\sigma}_2\) denote min\(\{ d(u) + d(v)\mid uv \in E(G) \}\). The author shows that if \(G\) is connected and of order \(n \geq 43\) such that the line graph \(L(G)\) is Hamiltonian and \(\overline {\sigma}_2> 2(n/5 - 1)\), then \(L(G)\) is pancyclic. This settles a conjecture of Benhocine et al. For a connected graph
Daniela Ferrero, Linda Lesniak
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