Aneta Dudek, Artur Szymański, Małgorzata Zwonek (2008)
Discussiones Mathematicae Graph Theory
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Let us call a G (H,k) graph vertex stable if it contains a subgraph H ever after removing any of its k vertices. By Q(H,k) we will denote the minimum size of an (H,k) vertex stable graph. In this paper, we are interested in finding Q(₃,k), Q(₄,k), and Q(Kₛ,k).
Luis Antonio Favaro, C. M. Mendes (1986)
Annales de l'institut Fourier
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In this paper, we give some examples which point to the non-existence of -global stable diagrams , compact. If : is fixed we define the -equivalence for maps and the corresponding -stability. The globalization procedure works and we can compare the -stability, -infinitesimal stability, and -homotopical stability. Also we give some characterization theorems for lower dimensions.
Levit, Vadim E., Mândrescu, Eugen (2005)
Acta Universitatis Apulensis. Mathematics - Informatics
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Lixin Cheng, Duanxu Dai, Yunbai Dong, Yu Zhou (2014)
Studia Mathematica
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Let X, Y be real Banach spaces and ε > 0. A standard ε-isometry f: X → Y is said to be (α,γ)-stable (with respect to for some α,γ > 0) if T is a linear operator with ||T|| ≤ α such that Tf- Id is uniformly bounded by γε on X. The pair (X,Y) is said to be stable if every standard ε-isometry f: X → Y is (α,γ)-stable for some α,γ > 0. The space X[Y] is said to be universally left [right]-stable if (X,Y) is always stable for every Y[X]. In this paper, we show that universally...
Aneta Dudek, Małgorzata Zwonek (2009)
Discussiones Mathematicae Graph Theory
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Let us call a graph G(H;k) vertex stable if it contains a subgraph H after removing any of its k vertices. In this paper we are interested in finding the (respectively ) vertex stable graphs with minimum size.
J.L. Fouquet, H. Thuillier, J.M. Vanherpe, A.P. Wojda (2013)
Discussiones Mathematicae Graph Theory
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A graph G is a (Kq, k) stable graph (q ≥ 3) if it contains a Kq after deleting any subset of k vertices (k ≥ 0). Andrzej ˙ Zak in the paper On (Kq; k)-stable graphs, ( doi:/10.1002/jgt.21705) has proved a conjecture of Dudek, Szyma´nski and Zwonek stating that for sufficiently large k the number of edges of a minimum (Kq, k) stable graph is (2q − 3)(k + 1) and that such a graph is isomorphic to sK2q−2 + tK2q−3 where s and t are integers such that s(q − 1) + t(q − 2) − 1 = k. We have...
Mustapha Chellali, Teresa W. Haynes, Lutz Volkmann (2010)
Discussiones Mathematicae Graph Theory
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Let k be a positive integer and G = (V(G),E(G)) a graph. A subset S of V(G) is a k-independent set of G if the subgraph induced by the vertices of S has maximum degree at most k-1. The maximum cardinality of a k-independent set of G is the k-independence number βₖ(G). A graph G is called β¯ₖ-stable if βₖ(G-e) = βₖ(G) for every edge e of E(G). First we give a necessary and sufficient condition for β¯ₖ-stable graphs. Then we establish four equivalent conditions for β¯ₖ-stable trees. ...
Raffaele Mosca (2012)
Discussiones Mathematicae Graph Theory
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The Maximum Stable Set (MS) problem is a well known NP-hard problem. However different graph classes for which MS can be efficiently solved have been detected and the augmenting graph technique seems to be a fruitful tool to this aim. In this paper we apply a recent characterization of minimal augmenting graphs [22] to prove that MS can be solved for -free graphs in polynomial time, extending some known results.
Marie Dvorská (2013)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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The aim of this paper is to summarize basic facts about -stable at a point vector functions and existing results for certain vector constrained programming problem with -stable data.
J. Auslander, P. Seibert (1964)
Annales de l'institut Fourier
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Les auteurs étudient la notion de prolongement au sens de T. Ura et ses relations avec la notion d’ensembles positivement invariants. La stabilité au sens de Liapounoff est équivalente à l’invariance par prolongement. Les auteurs dégagent ensuite la notion de “prolongements abstraits” et les notions de stabilité correspondantes; la stabilité absolue (associée au prolongement minimal transitif) et la stabilité asymptotique jouent un rôle important.
Marta Borowiecka-Olszewska, Jolanta K. Misiewicz (2003)
Discussiones Mathematicae Probability and Statistics
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In this paper, we consider a symmetric α-stable p-sub-stable two-dimensional random vector. Our purpose is to show when the function is a characteristic function of such a vector for some p and α. The solution of this problem we can find in [3], in the language of isometric embeddings of Banach spaces. Our proof is based on simple properties of stable distributions and some characterization given in [4].
I. E. Zverovich, O. I. Zverovich (2004)
The Yugoslav Journal of Operations Research
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Stutson, Donna, Vatsala, A.S. (1996)
Journal of Applied Mathematics and Stochastic Analysis
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Jintang Li (2003)
Colloquium Mathematicae
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Let Mⁿ (n ≥ 3) be an n-dimensional complete hypersurface in a real space form N(c) (c ≥ 0). We prove that if the sectional curvature of M satisfies the following pinching condition: , where δ = 1/5 for n ≥ 4 and δ = 1/4 for n = 3, then there are no stable currents (or stable varifolds) in M. This is a positive answer to the well-known conjecture of Lawson and Simons.