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Start Over Author "Rutherford, Carrie G." Topic abstract algebra
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1. PANCYCLICITY WHEN EACH CYCLE MUST PASS EXACTLY k HAMILTON CYCLE CHORDS.

Author

CHAOUCHE, FATIMA AFFIF, RUTHERFORD, CARRIE G., and WHITTY, ROBIN W.

Subjects
*GRAPH theory, *MATHEMATICAL bounds, *ABSTRACT algebra, *MATHEMATICAL analysis, *NUMERICAL analysis
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 Ωnn1/k on the growth rate. [ABSTRACT FROM AUTHOR]

Published
2015
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