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English version:
Journal of Applied and Industrial Mathematics, 2017, 11:3, 421-430

Volume 24, No 3, 2017, P. 61-79

UDC 519.174.3
D. B. Mokeev
On König graphs with respect to $P_4$

Abstract:
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.

DOI: 10.17377/daio.2017.24.561

Dmitry B. Mokeev 1,2
1. Lobachevsky Nizhny Novgorod State University,
23 Gagarin Ave., 603950 Nizhny Novgorod, Russia
2. Higher School of Economics in Nizhny Novgorod,
25/12 Bolshaya Pechyorskaya St., 603155 Nizhny Novgorod, Russia
e-mail: MokeevDB@gmail.com

Revised 24 January 2017

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