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Regular version of the site

Article

Konig graphs with respect to the 4-path and Its spanning supergraphs

Journal of Applied and Industrial Mathematics. 2019. Vol. 13. No. 1. P. 85-92.

We describe the class of graphs whose each 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 so-called pendant subgraphs, isomorphic to triangles and stars.