Geodesic
On K\"onig graphs with respect to~$P_4$
Diskretnyj analiz i issledovanie operacij, Tome 24 (2017) no. 3, pp. 61-79

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We describe the class of graphs whose every induced subgraph has the property: The maximum number of disjoint induced $4$-paths is equal to the minimum size of the set of the vertices such that each $4$-path contains at least one of them. The description is based on the operation of replacing vertices by cographs which is to the vertices of the graphs obtained from bipartite graphs by subdividing their cycle edges. Bibliogr. 13.
Keywords: packing of subgraphs, vertex covering of subgraphs, $4$-path, König graph. 
@article{DA_2017_24_3_a3,
     author = {D. B. Mokeev},
     title = {On {K\"onig} graphs with respect to~$P_4$},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {61--79},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2017_24_3_a3/}
}
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D. B. Mokeev. On K\"onig graphs with respect to~$P_4$. Diskretnyj analiz i issledovanie operacij, Tome 24 (2017) no. 3, pp. 61-79. http://geodesic.mathdoc.fr/item/DA_2017_24_3_a3/