The annihilation number a of a graph is an upper bound of the independence number α of a graph. In this article we characterize graphs with equal independence and annihilation numbers. In particular, we show that α = a if, and only if, either (1) a ≥ n2 and α ′ = a, or (2) a < n2 and there is a vertex v ∈ V (G) such that α(G − v) = a(G), where α is the critical independence number of the graph....

A pseudo [2, b]-factor of a graph G is a spanning subgraph in which each component C on at least three vertices verifies 2 ≤ dC(x) ≤ b, for every vertex x in C. The main contibution of this paper, is to give an upper bound to the number of components that are edges or vertices in a pseudo [2, b]-factor of a graph G. Given an integer b ≥ 4, we show that a graph G with minimum degree δ, independe...

The first application of Szemerédi’s powerful regularity method was the following celebrated Ramsey-Turán result proved by Szemerédi in 1972: any K4-free graph on n vertices with independence number o(n) has at most ( 18 +o(1))n 2 edges. Four years later, Bollobás and Erdős gave a surprising geometric construction, utilizing the isoperimetric inequality for the high dimensional sphere, of a K4-...

CONTEXT AND OBJECTIVE Muscle strength and functional independence are considered to be determinants of frailty levels among elderly people. The aim here was to compare lower-limb muscle strength (LLMS) with functional independence in relation to sex, age and number of frailty criteria, and to ascertain the influence of these variables on elderly outpatients' independence. DESIGN AND SETTING Q...

In this paper we present upper bounds on the differences between the independence, domination and irredundance parameters of a graph. For example, using the Brooks theorem on the chromatic number, we show that for any graph G of order n with maximum degree ∆ ≥ 2 IR(G)− β(G) ≤ ⌊ ∆− 2 2∆ n ⌋ , where β(G) and IR(G) are the independence number and the upper irredundance number of a graph G, respect...