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Start Over Author "Rutherford, Carrie G." Journal discussiones mathematicae graph theory
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1. Pancyclicity when each Cycle Must Pass Exactly k Hamilton Cycle Chords

Author

Affif Chaouche Fatima, Rutherford Carrie G., and Whitty Robin W.

Subjects
extremal graph theory, pancyclic graph, hamilton cycle, Mathematics, QA1-939
Abstract

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.

Published
2015
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