On vertex stability of complete k-partite graphs

• Autorzy: Nikodem M.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2015.35.6.907

• Języki publikacji: EN

Abstrakty

EN

Let H be any graph. We say that graph G is H-stable if G — u contains a subgraph isomorphic to H for an arbitrary chosen u ∈ V(G). We characterize all H-stable graphs of minimal size where H is any complete k-partite graph. Thus, we generalize the results of Dudek and Żak regarding complete bipartite graphs.

Słowa kluczowe

EN

vertex stability; minimal stable graphs; complete k-partite graphs

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2015
• Tom: Vol. 35, no. 6
• Strony: 907--914
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Nikodem M.

• AGH University of Science and Technology Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krakow, Poland

Bibliografia

• [1] S. Cichacz, A. Gorlich, M. Nikodem, A. Żak, Lower bound on the size of (H; 1)-vertex stable graphs, Discrete Math 312 (2012) 20, 3026-3029.
• [2] S. Cichacz, A. Gorlich, M. Zwonek, A. Żak, On (Cn,k) stable graphs, Electron. J. Comb. 18 (2011) 1, #P205.
• [3] R. Diestel, Graph Theory, 2nd ed., Springer-Verlag, 2000.
• [4] A. Dudek, A. Szymański, M. Zwonek, (H,k) stable graphs with minimum size, Discuss. Math. Graph Theory 28 (2008), 137-149.
• [5] A. Dudek, M. Zwonek, (H,k) stable bipartite graphs with minimum size, Discuss. Math. Graph Theory 29 (2009), 573-581.
• [6] A. Dudek, A. Żak, On vertex stability with regard to complete bipartite subgraphs, Discuss. Math. Graph Theory 30 (2010), 663-669.
• [7] J.-L. Fouquet, H. Thuillier, J-M. Vanherpe, A.P. Wojda, On (Kq; k) vertex stable graphs with minimum size, Discrete Math. 312 (2012) 14, 2109-2118.
• [8] J.-L. Fouquet, H. Thuillier, J-M. Vanherpe, A.P. Wojda, On (Kq; k) vertex stable graphs with small k, Electron. J. Comb. 19 (2012) 2, #P50.
• [9] A. Żak, On (Kq;k)-stable graphs, J. Graph Theory 74 (2013) 2, 216-221.
• [10] A. Żak, General lower bound on the size of (H;k)-stable graphs, J. Comb. Optim. 29 (2015), 367-372.