Stability-type results for hereditary properties

Stability-type results for hereditary properties

The classical Stability Theorem of Erdős and Simonovits can be stated as follows. For a monotone graph property P, let t ≥ 2 be such that t + 1 = min{χ(H) : H / ∈ P}. Then any graph G∗ ∈ P on n vertices, which was obtained by removing at most (1t + o(1)) ( n 2 ) edges from the complete graph G = Kn, has edit distance o(n) to Tn(t), the Turán graph on n vertices with t parts. In this paper we ex...

Supersaturation for hereditary properties

Let F be a collection of r-uniform hypergraphs, and let 0 < p < 1. It is known that there exists c = c(p,F) such that the probability of a random r-graph in G(n, p) not containing an induced subgraph from F is 2(−c+o(1))( n r). Let each r-graph in F have at least t vertices. We show that in fact for every > 0, there exists δ = δ( , p,F) > 0 such that the probability of a random r-graph in G(n, ...

Stability results for set solution of fuzzy integro-differential systems

Nordhaus-Gaddum type results for the Harary index of graphs

The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ ...

Stability Results for Some Functional Equations of Quadratic-type

We present some theorems of stability, in the Hyers-UlamRassias sense, for functional equations of quadratic-type, extending the results from [2], [8], [16], [19] and [20]. There are used both the direct and the fixed point methods. 2000 Mathematics Subject Classification: 39B52, 39B62, 39B82, 47H09.