Some Variations of Perfect Graphs

• Autorzy: Magda Dettlaff , Magdalena Lemańska , Gabriel Semanišin , Rita Zuazua
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

k-path vertex cover; distance k-domination number; perfect graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2016
• Tom: 36
• Numer: 3
• Strony: 661-668

Daty

wydano

2016-08-01

otrzymano

2015-03-03

poprawiono

2015-09-23

zaakceptowano

2015-10-09

online

2016-07-06

Twórcy

autor

Magda Dettlaff

• Faculty of Applied Physics and Mathematics Gdańsk University of Technology ul. Narutowicza 11/12, 80–233 Gdańsk, Poland,

autor

Magdalena Lemańska

• Faculty of Applied Physics and Mathematics Gdańsk University of Technology ul. Narutowicza 11/12, 80–233 Gdańsk, Poland

autor

Gabriel Semanišin

• Institute of Computer Science P.J. Šafárik University Jesenná 5, 041 54 Košice, Slovakia,

autor

Rita Zuazua

• Faculty of Science National Autonomous University of Mexico Av. Universidad 3000, Mexico City, Mexico,

Bibliografia

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• [5] T. Haynes, S. Hedetniemi and P. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, 1998).
• [6] M.A. Henning, O.R. Oellermann and H.C. Swart, Bounds on distance domination parameters, J. Combin. Inform. System Sci. 16 (1991) 11-18.
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• [8] L. Volkmann, On graphs with equal domination and covering numbers, Discrete Appl. Math. 51 (1994) 211-217. doi:10.1016/0166-218X(94)90110-4[Crossref]
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Identyfikatory

DOI

10.7151/dmgt.1880