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.
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The authors were supported by the Russian Foundation for Basic Research (project no. 18–31–20001-mol-a-ved).
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Translated by Ya.A. Kopylov
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Mokeev, D.B., Malyshev, D.S. On the König Graphs for a \(\boldsymbol 5 \)-Path and Its Spanning Supergraphs. J. Appl. Ind. Math. 14, 369–384 (2020). https://doi.org/10.1134/S1990478920020143
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DOI: https://doi.org/10.1134/S1990478920020143