Authors
Elad Aigner-Horev, Gil Levy
Publication date
2021/5
Journal
Combinatorics, Probability and Computing
Volume
30
Issue
3
Pages
412-443
Publisher
Cambridge University Press
Description
We employ the absorbing-path method in order to prove two results regarding the emergence of tight Hamilton cycles in the so-called two-path or cherry-quasirandom 3-graphs.Our first result asserts that for any fixed real α > 0, cherry-quasirandom 3-graphs of sufficiently large order n having minimum 2-degree at least α(n – 2) have a tight Hamilton cycle.Our second result concerns the minimum 1-degree sufficient for such 3-graphs to have a tight Hamilton cycle. Roughly speaking, we prove that for every d, α > 0 satisfying d + α > 1, any sufficiently large n-vertex such 3-graph H of density d and minimum 1-degree at least has a tight Hamilton cycle.
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Scholar articles
E Aigner-Horev, G Levy - Combinatorics, Probability and Computing, 2021