The primary objective of this study was to propose a functional discrete mathematical model for analyzing folklore fairy tales. Within this model, characters are denoted as vertices, and explicit instances of communication – both verbal and non-verbal – within the text are depicted as edges. Upon examining a corpus of Eastern Slavic fairy tales in comparison to Chukchi fairy tales, unforeseen outcomes emerged. Notably, the constructed models seem to evade establishing certain connections between characters. Consequently, instances where the interactions among fairy tale characters would result in a non-planar graph structure are notably absent. To put it differently, the models refrain from incorporating sub-graphs delineated by the Kuratowski theorem governing planar graphs, specifically the minimal non-planar graphs Κ5 and Κ3,3. Remarkably, even in more extensive texts featuring a larger cast of characters, connections that would yield a non-planar graph pattern are consistently avoided. This leads to the formulation of a hypothesis positing that traditional folk tales adhere to a “planar narrative” design – an identifiable narrative variant characterized by inherent limitations in complexity. This design, in turn, appears deeply entrenched within the societal framework of the cultures that produced these folk narratives.

中文翻译：

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作为传统童话拓扑模型的平面图

本研究的主要目的是提出一个用于分析民间传说童话的函数离散数学模型。在这个模型中，字符被表示为顶点，文本中的明确的交流实例（包括口头和非口头）被描述为边缘。在将东斯拉夫童话故事集与楚科奇童话故事进行比较后，出现了意想不到的结果。值得注意的是，构建的模型似乎回避了在角色之间建立某些联系。因此，童话人物之间的相互作用会导致非平面图形结构的情况明显不存在。换句话说，模型不会合并由控制平面图的库拉托夫斯基定理所描述的子图，特别是最小非平面图 Κ5和 Κ3,3。值得注意的是，即使在具有更多字符的更广泛的文本中，也会始终避免产生非平面图形模式的连接。这导致提出一个假设，即传统民间故事遵循“平面叙事”设计——一种可识别的叙事变体，其特点是复杂性的固有局限性。反过来，这种设计似乎深深植根于产生这些民间叙事的文化的社会框架中。