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On partial descriptions of König graphs for odd paths and all their spanning supergraphs

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We consider graphs, which and all induced subgraphs of which possess the following property: the maximum number of disjoint paths on k vertices equals the minimum cardinality of vertex sets, covering all paths on k vertices. We call such graphs König for the k-path and all its spanning supergraphs. For each odd k, we reveal an infinite family of minimal forbidden subgraphs for them. Additionally, for every odd k, we present a procedure for constructing some of such graphs, based on the operations of adding terminal subgraphs and replacement of edges with subgraphs.

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Authors and Affiliations

  1. Lobachevsky State University of Nizhny Novgorod, 23 Gagarina ave., Nizhny Novgorod, Russia, 603950

    Dmitry B. Mokeev

  2. Laboratory of Algorithms and Technologies for Networks Analysis, National Research University Higher School of Economics, 136 Rodionova Str., Nizhny Novgorod, Russia, 603093

    Dmitry B. Mokeev & Dmitry S. Malyshev

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  1. Dmitry B. Mokeev
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  2. Dmitry S. Malyshev
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Correspondence to Dmitry S. Malyshev.

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The Sect. 3 was prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE). The Sect. 4 was funded by RFBR and BRFBR, Project Number 20-51-04001.

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Mokeev, D.B., Malyshev, D.S. On partial descriptions of König graphs for odd paths and all their spanning supergraphs. Optim Lett 16, 481–496 (2022). https://doi.org/10.1007/s11590-021-01771-8

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  • DOI: https://doi.org/10.1007/s11590-021-01771-8

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