Results 11 to 20 of about 1,031 (124)
Pancyclicity of hamiltonian line graphs [PDF]
Discrete Mathematics, 1995 AbstractLet f(n) be the smallest integer such that for every graph G of order n with minimum degree δ(G) > f(n), the line graph L(G) of G is pancyclic whenever L(G) is hamiltonian. Results are proved showing that f(n) = Θ(n13).
E. van Blanken +2 more
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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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Discussiones Mathematicae Graph Theory, 2015 For integers k and n with 2 ≤ k ≤ n − 1, a graph G of order n is k-path pancyclic if every path P of order k in G lies on a cycle of every length from k + 1 to n. Thus a 2-path pancyclic graph is edge-pancyclic.
Bi Zhenming, Zhang Ping
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Pancyclicity of Hamiltonian graphs
Journal of the European Mathematical SocietyAn n -vertex graph is Hamiltonian if it contains a cycle that covers all of its vertices, and it is pancyclic if it contains cycles of all lengths from 3 up to
Nemanja Draganić +2 more
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Pancyclicity in claw-free graphs [PDF]
Discrete Mathematics, 2002 AbstractIn this paper, we present several conditions for K1,3-free graphs, which guarantee the graph is subpancyclic. In particular, we show that every K1,3-free graph with a minimum degree sum δ2>23n+1−4; every {K1,3,P7}-free graph with δ2⩾9; every {K1,3,Z4}-free graph with δ2⩾9; and every K1,3-free graph with maximum degree Δ, diam(G)
Ronald J. Gould, Florian Pfender
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The Completion Numbers of Hamiltonicity and Pancyclicity in Random Graphs
Random Structures &Algorithms, Volume 66, Issue 2, March 2025.ABSTRACT Let μ(G)$$ \mu (G) $$ denote the minimum number of edges whose addition to G$$ G $$ results in a Hamiltonian graph, and let μ^(G)$$ \hat{\mu}(G) $$ denote the minimum number of edges whose addition to G$$ G $$ results in a pancyclic graph. We study the distributions of μ(G),μ^(G)$$ \mu (G),\hat{\mu}(G) $$ in the context of binomial random ...
Yahav Alon, Michael Anastos
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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 Chan +3 more
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Journal of Combinatorial Theory, Series B, 1976 Abstract A 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)| ≥ n 2 4 , where n = |V(G)|. Then G is either pancyclic or else is the complete bipartite graph K n 2 , n 2 .
J. A. Bondy, A. W. Ingleton
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On circuits and pancyclic line graphs [PDF]
Journal of Graph Theory, 1986 AbstractClark proved that L(G) is hamiltonian if G is a connected graph of order n ≥ 6 such that deg u + deg v ≥ n – 1 – p(n) for every edge uv of G, where p(n) = 0 if n is even and p(n) = 1 if n is odd. Here it is shown that the bound n – 1 – p(n) can be decreased to (2n + 1)/3 if every bridge of G is incident with a vertex of degree 1, which is a ...
Abdelhamid Benhocine +3 more
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On pancyclic line graphs [PDF]
Czechoslovak Mathematical Journal, 1978 Ladislav Nebeský
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