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 $\alpha \left({\matrix{{n - 1} \cr 2 \cr } } \right)$ has a tight Hamilton cycle.

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樱桃准随机 3 均匀超图中的紧汉密尔顿循环

我们采用吸收路径方法来证明关于在所谓的紧汉密尔顿循环中出现的两个结果两路要么樱桃-quasirandom 3-graphs。我们的第一个结果断言，对于任何固定实数α> 0，足够大阶的cherry-quasirandom 3-graphn至少有 2 度α(n– 2) 有一个紧的汉密尔顿循环。我们的第二个结果涉及最小 1 度，足以让这样的 3-图有一个紧的汉密尔顿循环。粗略地说，我们证明对于每个d,α> 0 满意d+α> 1，任何足够大的n-vertex 这样的 3-graphH密度的d至少 1 度$\alpha \left({\matrix{{n - 1} \cr 2 \cr } } \right)$有一个紧的汉密尔顿循环。