Displaying similar documents to “Counting the number of elements in the mutation classes of A n -quivers.”

Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords

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.