Results 1 to 10 of about 782 (111)

Rainbow vertex pair-pancyclicity of strongly edge-colored graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2023
An edge-colored graph is \emph{rainbow }if no two edges of the graph have the same color. An edge-colored graph $G^c$ is called \emph{properly colored} if every two adjacent edges of $G^c$ receive distinct colors in $G^c$.
Peixue Zhao, Fei Huang
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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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Fan's condition on induced subgraphs for circumference and pancyclicity [PDF]

Opuscula Mathematica, 2017
Let \(\mathcal{H}\) be a family of simple graphs and \(k\) be a positive integer. We say that a graph \(G\) of order \(n\geq k\) satisfies Fan's condition with respect to \(\mathcal{H}\) with constant \(k\), if for every induced subgraph \(H\) of \(G ...
Wojciech Wideł
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Edge condition for hamiltonicity in balanced tripartite graphs [PDF]

Opuscula Mathematica, 2009
A well-known theorem of Entringer and Schmeichel asserts that a balanced bipartite graph of order \(2n\) obtained from the complete balanced bipartite \(K_{n,n}\) by removing at most \(n-2\) edges, is bipancyclic.
Janusz Adamus
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On regular subgraphs of augmented cubes

AKCE International Journal of Graphs and Combinatorics, 2020
The n-dimensional augmented cube AQn is a variation of the hypercube It is a -regular and -connected graph on vertices. One of the fundamental properties of AQn is that it is pancyclic, that is, it contains a cycle of every length from 3 to In this paper,
Amruta Shinde, Y. M. Borse
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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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A Fan-Type Heavy Pair Of Subgraphs For Pancyclicity Of 2-Connected Graphs

Discussiones Mathematicae Graph Theory, 2016
Let G be a graph on n vertices and let H be a given graph. We say that G is pancyclic, if it contains cycles of all lengths from 3 up to n, and that it is H-f1-heavy, if for every induced subgraph K of G isomorphic to H and every two vertices u, v ∈ V (K)
Wideł Wojciech
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A Triple of Heavy Subgraphs Ensuring Pancyclicity of 2-Connected Graphs

Discussiones Mathematicae Graph Theory, 2017
A graph G on n vertices is said to be pancyclic if it contains cycles of all lengths k for k ∈ {3, . . . , n}. A vertex v ∈ V (G) is called super-heavy if the number of its neighbours in G is at least (n+1)/2.
Wide Wojciech
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Pancyclicity When Each Cycle Contains k Chords

Discussiones Mathematicae Graph Theory, 2019
For integers n ≥ k ≥ 2, let c(n, k) be the minimum number of chords that must be added to a cycle of length n so that the resulting graph has the property that for every l ∈ {k, k + 1, . . .
Taranchuk Vladislav
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Local properties of graphs that induce global cycle properties [PDF]

Opuscula Mathematica
A graph \(G\) is locally Hamiltonian if \(G[N(v)]\) is Hamiltonian for every vertex \(v\in V(G)\). In this note, we prove that every locally Hamiltonian graph with maximum degree at least \(|V(G)| - 7\) is weakly pancyclic.
Yanyan Wang, Xiaojing Yang
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