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Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords
Discussiones Mathematicae Graph Theory, 2015 It is known that Θ(log n) chords must be added to an n-cycle to produce a pancyclic graph; for vertex pancyclicity, where every vertex belongs to a cycle of every length, Θ(n) chords are required.
Affif Chaouche Fatima +2 more
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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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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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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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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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On the pancyclicity of 1-tough graphs [PDF]
Discrete Mathematics Letters, 2020 Rao Li
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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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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
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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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Generating random graphs in biased Maker-Breaker games [PDF]
, 2015 We present a general approach connecting biased Maker-Breaker games and problems about local resilience in random graphs. We utilize this approach to prove new results and also to derive some known results about biased Maker-Breaker games. In particular,
Ferber, Asaf +2 more
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