Results 31 to 40 of about 1,777 (160)
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 +2 more
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Hamiltonicity and pancyclicity of superclasses of claw-free graphs
Filomat, 2023 A graph G is called to be fully cycle extendable graph [3] if each vertex of G belongs to a triangle and for any cycle C with |V(C)| < |V(G)| there exists a cycle C? in G such that V(C) ? V(C?) and |V(C?)| = |V(C)|+1. In this paper, we show that every
Abdelkader Sahraoui, Zineb Benmeziane
semanticscholar +1 more source
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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Heavy subgraphs, stability and hamiltonicity [PDF]
, 2016 Let $G$ be a graph. Adopting the terminology of Broersma et al. and \v{C}ada, respectively, we say that $G$ is 2-heavy if every induced claw ($K_{1,3}$) of $G$ contains two end-vertices each one has degree at least $|V(G)|/2$; and $G$ is o-heavy if every
Li, Binlong, Ning, Bo
core +4 more sources
Discrete Applied Mathematics, 1999 AbstractLet G be a graph of order n. A graph G is called pancyclic if it contains a cycle of length k for every 3⩽k⩽n, and it is called vertex pancyclic if every vertex is contained in a cycle of length k for every 3⩽k⩽n. In this paper, we shall present different sufficient conditions for graphs to be vertex pancyclic.
Ingo Schiermeyer +3 more
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On pancyclism in hamiltonian graphs
Discrete Mathematics, 2002 AbstractWe investigate the set of cycle lengths occurring in a hamiltonian graph with at least one or two vertices of large degree. We prove that in every case this set contains all the integers between 3 and some t, where t depends on the order of the graph and the degrees of vertices.
Mekkia Kouider, Antoni Marczyk
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Tight Hamilton Cycles in Random Uniform Hypergraphs [PDF]
, 2010 In this paper we show that $e/n$ is the sharp threshold for the existence of tight Hamilton cycles in random $k$-uniform hypergraphs, for all $k\ge 4$. When $k=3$ we show that $1/n$ is an asymptotic threshold.
Dudek, Andrzej, Frieze, Alan
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Computing Edge Weights of Magic Labeling on Rooted Products of Graphs
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 Labeling of graphs with numbers is being explored nowadays due to its diverse range of applications in the fields of civil, software, electrical, and network engineering. For example, in network engineering, any systems interconnected in a network can be converted into a graph and specific numeric labels assigned to the converted graph under certain ...
Jia-Bao Liu +3 more
wiley +1 more source
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.
Carsten Thomassen, Roland Häggkvist
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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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