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On the König Graphs for a $$\boldsymbol 5 $$ -Path and Its Spanning Supergraphs
Journal of Applied and Industrial Mathematics Pub Date : 2020-07-10 , DOI: 10.1134/s1990478920020143
D. B. Mokeev , D. S. Malyshev

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:

$$ \ boldsymbol 5 $$-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。
更新日期:2020-07-10
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