Abstract

We describe the hereditary class of graphs whose every subgraph has the property that the maximum number of disjoint \(5\)-paths (paths on \(5 \) vertices) is equal to the minimum size of the sets of vertices having nonempty intersection with the vertex set of each \(5 \)-path. We describe this class in terms of the “forbidden subgraphs” and give an alternative description, using some operations on pseudographs.

中文翻译：

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$$ \ boldsymbol 5 $$-路径的König图及其跨度超图

摘要

我们描述图的遗传类，其每个子图具有以下性质：不相交的\（5 \）- paths（\（5 \）顶点上的路径 ）的最大数目等于具有非空交点的顶点集的最小大小与每个\（5 \）-路径的顶点集。我们根据“禁止子图”来描述此类，并使用对伪图的一些操作来给出替代描述。