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Edge-pancyclicity of pancake graph
International Journal of Computer Mathematics: Computer Systems Theory, 2020Pancylicity was introduced by Bondy in 1971. A graph G with vertex set V ( G ) and edge set E ( G ) is pancyclic if it contains cycles of lengths l, for 3 ≤ l ≤ | V ( G ) | .
Chun-Nan Hung +3 more
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2016
Recall that a pancyclic graph is called uniquely pancyclic, or UPC, if it contains exactly one cycle of every possible length. In 1973, Roger Entringer asked (see Bondy (J. Combinatorial Theory (B) 11:80–84, 1971), p. 247), for what orders do UPC graphs exist?
John C. George +2 more
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Recall that a pancyclic graph is called uniquely pancyclic, or UPC, if it contains exactly one cycle of every possible length. In 1973, Roger Entringer asked (see Bondy (J. Combinatorial Theory (B) 11:80–84, 1971), p. 247), for what orders do UPC graphs exist?
John C. George +2 more
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Generalizing Pancyclic and k-Ordered Graphs
Graphs and Combinatorics, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Faudree, Ralph J. +3 more
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Pancyclicity of Strong Products of Graphs
Graphs and Combinatorics, 2004A graph with \(n\) vertices is pancyclic if it contains a cycle of length \(s\) for all \(s\), \(3\leq s\leq n\). In particular, a pancyclic graph is Hamiltonian. The {strong product} of \(k\) graphs \(G_1=(V_1,E_1),\dots, G_k=(V_k,E_k)\) is the graph \(G_1\times\cdots\times G_k\) with \(V_1\times\cdots \times V_k\) as set of vertices and two vertices \
Král, Daniel +3 more
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Erratum to “Pancyclicity of recursive circulant graphs”
Information Processing Letters, 2002Correction of ibid. 81, 187--190 (2002; Zbl 1013.68137).
Araki, Tom, Shibata, Yukio
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Acta Mathematicae Applicatae Sinica, 1987
A graph with n vertices is pancyclic if it contains for every k, \(3\leq k\leq n,\) a circuit of length k. A graph is vertex pancyclic if every vertex is contained in a circuit of length k for every k, \(3\leq k\leq n\). In the paper are given some sufficient conditions for a graph which is a line graph of a finite graph G to be (vertex) pancyclic.
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A graph with n vertices is pancyclic if it contains for every k, \(3\leq k\leq n,\) a circuit of length k. A graph is vertex pancyclic if every vertex is contained in a circuit of length k for every k, \(3\leq k\leq n\). In the paper are given some sufficient conditions for a graph which is a line graph of a finite graph G to be (vertex) pancyclic.
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Pancyclicity of recursive circulant graphs
Information Processing Letters, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Araki, Toru, Shibata, Yukio
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Pancyclicity of connected circulant graphs
Journal of Graph Theory, 1996The following results are shown for connected circulant graphs \(G\): (1) If \(G\) has at least two jumps, then every edge of \(G\) lies in a cycle of each even length \(i, i\geq 4\). (2) If the smallest cycle of \(G\) is a triangle, then \(G\) is pancyclic. To show these results, cycles of the specified lengths are all explicitly given.
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