A problem concerning -pancyclic graphs
Vasil Jacoš, Stanislav Jendroľ (1974)
Matematický časopis
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Vasil Jacoš, Stanislav Jendroľ (1974)
Matematický časopis
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Eckhard Steffen (2001)
Mathematica Slovaca
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J. Adrian Bondy, Hajo J. Broersma, Jan van den Heuvel, Henk Jan Veldman (2002)
Discussiones Mathematicae Graph Theory
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An (edge-)weighted graph is a graph in which each edge e is assigned a nonnegative real number w(e), called the weight of e. The weight of a cycle is the sum of the weights of its edges, and an optimal cycle is one of maximum weight. The weighted degree w(v) of a vertex v is the sum of the weights of the edges incident with v. The following weighted analogue (and generalization) of a well-known result by Dirac for unweighted graphs is due to Bondy and Fan. Let G be a 2-connected weighted...
Terry A. McKee (2012)
Discussiones Mathematicae Graph Theory
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A graph is edge cycle extendable if every cycle C that is formed from edges and one chord of a larger cycle C⁺ is also formed from edges and one chord of a cycle C' of length one greater than C with V(C') ⊆ V(C⁺). Edge cycle extendable graphs are characterized by every block being either chordal (every nontriangular cycle has a chord) or chordless (no nontriangular cycle has a chord); equivalently, every chord of a cycle of length five or more has a noncrossing chord.
Eppstein, David (2007)
Journal of Graph Algorithms and Applications
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A. Benkouar, Y. Manoussakis, V. Th. Paschos, R. Saad (1996)
RAIRO - Operations Research - Recherche Opérationnelle
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Ruskey, F., Sawada, Joe (2003)
The Electronic Journal of Combinatorics [electronic only]
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Fatima Affif Chaouche, Carrie G. Rutherford, Robin W. Whitty (2015)
Discussiones Mathematicae Graph Theory
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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. A possibly ‘intermediate’ variation is the following: given k, 1 ≤ k ≤ n, how many chords must be added to ensure that there exist cycles of every possible length each of which passes exactly k chords? For fixed k, we establish a lower bound of ∩(n1/k) on the growth rate.
Lai, Chunhui (2001)
The Electronic Journal of Combinatorics [electronic only]
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