Geodesic
K\"onig graphs with respect to the 4-path and~its~spanning supergraphs
Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 1, pp. 74-88

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We describe the class of graphs whose every subgraph has the next property: The maximal number of disjoint 4-paths is equal to the minimal cardinality of sets of vertices such that every 4-path in the subgraph contains at least one of these vertices. We completely describe the set of minimal forbidden subgraphs for this class. Moreover, we present an alternative description of the class based on the operations of edge subdivision applied to bipartite multigraphs and the addition of the so-called pendant subgraphs, isomorphic to triangles and stars. Illustr. 1, bibliogr. 19.
Keywords: subgraph packing, vertex cover of a subgraph, 4-path, König graph. 
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     author = {D. S. Malyshev and D. B. Mokeev},
     title = {K\"onig graphs with respect to the 4-path and~its~spanning supergraphs},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {74--88},
     publisher = {mathdoc},
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     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2019_26_1_a4/}
}
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D. S. Malyshev; D. B. Mokeev. K\"onig graphs with respect to the 4-path and~its~spanning supergraphs. Diskretnyj analiz i issledovanie operacij, Tome 26 (2019) no. 1, pp. 74-88. http://geodesic.mathdoc.fr/item/DA_2019_26_1_a4/