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Pancyclicity of the n-Generalized Prism over Skirted Graphs
Symmetry, 2022 A side skirt is a planar rooted tree T, T≠P2, where the root of T is a vertex of degree at least two, and all other vertices except the leaves are of degree at least three.
Artchariya Muaengwaeng +2 more
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Discrete Applied Mathematics, 2007 A shortest path connecting two vertices u and v is called a u-v geodesic. The distance between u and v in a graph G, denoted by d"G(u,v), is the number of edges in a u-v geodesic. A graph G with n vertices is panconnected if, for each pair of vertices u,[email protected]?V(G) and for each integer k with d"G(u,v)=
Hung-Chang,C. A. +3 more
openaire +3 more sources
Discrete Mathematics, 2001 Abstract We show that for every 3 -connected cubic graph G , the prism G×K 2 has cycles of every even length. Furthermore, if G has a triangle, then G×K 2 is pancyclic.
Michael A. Henning, Wayne Goddard
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Pancyclicity of randomly perturbed digraph
JUSTC, 2022 Dirac’s theorem states that if a graph G on n vertices has a minimum degree of at least \begin{document}$\displaystyle \frac{n}{2}$\end{document}, then G contains a Hamiltonian cycle. Bohman et al.
Zelin Ren, Xinmin Hou
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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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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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Local properties of graphs that induce global cycle properties [PDF]
Opuscula MathematicaA 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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On pancyclic arcs in hypertournaments
Discrete Applied Mathematics, 2016 A k -hypertournament H on n vertices with 2 ź k ź n is a pair H = ( V , A H ) , where V is a set of n vertices and A H is a set of k -tuples of vertices, called arcs, such that for any k -subset S of V , A H contains exactly one of the k ! k -tuples whose entries belong to S .
Hongwei Li +3 more
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On the geodetic and the hull numbers in strong product graphs [PDF]
, 2010 A set S of vertices of a connected graph G is convex, if for any pair of vertices u; v 2 S, every shortest path joining u and v is contained in S . The convex hull CH(S) of a set of vertices S is defined as the smallest convex set in G containing S.
Caceres, Jose +4 more
core +2 more sources