Motivated by the long-standing and wide open pancyclicity conjectures of Bondy and Malkevitch, we study the cycle spectra of contraction-critically 4-connected planar graphs. We show that every contraction-critically 4-connected planar graph on n vertices contains a cycle of length k for every \(k \in \big \{\lfloor \frac{n}{2} \rfloor - \lceil \frac{n}{108} \rceil , \dots , \lfloor \frac{n}{2} \rfloor + \lfloor \frac{n}{36} \rfloor \big \} \cup \big \{\frac{2}{3} n, \dots , n\big \}\).

中文翻译：

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收缩临界 4-连通平面图的循环谱

受 Bondy 和 Malkevitch 长期存在且广泛开放的泛周期性猜想的启发，我们研究了收缩临界 4 连通平面图的循环谱。我们表明，对于每个\(k \in \big \{\lfloor \frac{n}{2} \rfloor - \lceil \frac{，n个顶点上的每个收缩临界 4-连通平面图都包含一个长度为k的循环n}{108} \rceil , \dots , \lfloor \frac{n}{2} \rfloor + \lfloor \frac{n}{36} \rfloor \big \} \cup \big \{\frac{2 }{3} n, \dots , n\big \}\)。