Results 61 to 70 of about 635 (107)

Pancyclism in hamiltonian graphs

Discrete Mathematics, 1991
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Denise Amar, Evelyne Flandrin, Irène Fournier, Anne Germa   +3 more
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On pancyclism of hamiltonian graphs

Electronic Notes in Discrete Mathematics, 2000
Abstract Let n and Δ be two integers with Δ ≤ n − 1. We study the set of cycle lengths occurring in any hamiltonian graph G of order n and maximum degree Δ. We show that for the case n/2+1 ≤ Δ ≤ 2n-2/3 this set contains all the integers belonging to the union [3, 2Δ-n+2] ∪ [n-Δ+ 2,Δ+1], and for 2n−2 3 ≤ Δ ≤ n − 1 it contains every integer ...
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Forbidden subgraphs for chorded pancyclicity

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, Ronald J. Gould, Victor Larsen   +2 more
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On k-path pancyclic graphs

Discussiones Mathematicae Graph Theory, 2015
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Bi Zhenming, Zhang Ping
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Pancyclicity of hamiltonian line graphs

Discrete Mathematics, 1995
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van Blanken, E., van den Heuvel, J.P.M., Veldman, H.J.   +2 more
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Global cycle properties in graphs with large minimum clustering coefficient

, 2016
The clustering coefficient of a vertex in a graph is the proportion of neighbours of the vertex that are adjacent. The minimum clustering coefficient of a graph is the smallest clustering coefficient taken over all vertices.
Borchert, Adam, Nicol, Skylar, Oellermann, Ortrud R.   +2 more
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Pancyclic graphs I

Journal of Combinatorial Theory, Series B, 1971
AbstractA graph G with vertex set V(G) and edge set E(G) is pancyclic if it contains cycles of all lengths l, 3 ≤ l ≤ | V(G) |.Theorem. Let G be Hamiltonian and suppose that |E(G)| ≥ n24, where n = |V(G)|. Then G is either pancyclic or else is the complete bipartite graph Kn2,n2.As a corollary to this theorem it is shown that the Ore conditions for a ...
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On pancyclic digraphs

Journal of Combinatorial Theory, Series B, 1976
AbstractWe show that a strongly connected digraph with n vertices and minimum degree ⩾ n is pancyclic unless it is one of the graphs Kp,p. This generalizes a result of A. Ghouila-Houri. We disprove a conjecture of J. A. Bondy by showing that there exist hamiltonian digraphs with n vertices and 12n(n + 1) – 3 edges which are not pancyclic.
Häggkvist, Roland, Thomassen, Carsten
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Chorded k-pancyclic and weakly k-pancyclic graphs

Discussiones Mathematicae Graph Theory
Summary: 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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Strongly pancyclic and dual-pancyclic graphs

Discussiones Mathematicae Graph Theory, 2009
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