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Some Variations of Perfect Graphs

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Dettlaff M., Lemańska M., Semanišin G., Zuazua R.

Discussiones Mathematicae Graph Theory

2016

tom 36

nr 3

661-668

We consider (ψk−γk−1)-perfect graphs, i.e., graphs G for which ψk(H) = γk−1(H) for any induced subgraph H of G, where ψk and γk−1 are the k-path vertex cover number and the distance (k − 1)-domination number, respectively. We study (ψk−γk−1)-perfect paths, cycles and complete graphs for k ≥ 2. Moreover, we provide a complete characterisation of (ψ2 − γ1)- perfect graphs describing the set of its forbidden induced subgraphs and providing the explicit characterisation of the structure of graphs belonging to this family.

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1 Discussiones Mathematicae Graph Theory

1 Dettlaff M.

1 Lemańska M.

1 Semanišin G.

1 Zuazua R.

1 2016

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Some Variations of Perfect Graphs