On -Pancyclic Graphs
Vasil Jacoš (1975)
Matematický časopis
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Vasil Jacoš (1975)
Matematický časopis
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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.
Jochen Harant, Stanislav Jendrol', Hansjoachim Walther (2008)
Discussiones Mathematicae Graph Theory
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For a 3-connected planar graph G with circumference c ≥ 44 it is proved that G has a cycle of length at least (1/36)c+(20/3) through any four vertices of G.
Vasil Jacoš, Stanislav Jendroľ (1974)
Matematický časopis
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Nikoghosyan, Zh.G. (2011)
International Journal of Mathematics and Mathematical Sciences
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Eckhard Steffen (2001)
Mathematica Slovaca
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