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Статья

König graphs for 3-paths and 3-cycles

Discrete Applied Mathematics. 2016. Vol. 204. P. 1-5.
Alekseev V. E., Mokeev D. B.

Given a set X, a König graph G for X is a graph with the following property: for every induced subgraph H of G, the maximum number of vertex-disjoint induced subgraphs from X in H is equal to the minimum number of vertices whose deletion from H results in a graph containing no graph in X as an induced subgraph. The purpose of this paper is to characterize all König graphs for X, where X has only the 3-path or X consists of the 3-path and 3-cycle. We give also polynomial-time algorithms for the recognition of König graphs for the 3-path and for finding the corresponding packing and cover numbers in graphs of this type.