The number of maximum primitive sets of integers

On primitive sets of squarefree integers

On the Counting Function of Primitive Sets of Integers

Erdo s has shown that for a primitive set A/N a # A 1 (a log a)<const. This implies that A(x)<x (log log x log log log x) for infinitely many x. We prove that this is best possible apart from a factor (log log log x). 1999 Academic Press

on the number of maximum independent sets of graphs

let $g$ be a simple graph. an independent set is a set ofpairwise non-adjacent vertices. the number of vertices in a maximum independent set of $g$ isdenoted by $alpha(g)$. in this paper, we characterize graphs $g$ with $n$ vertices and with maximumnumber of maximum independent sets provided that $alpha(g)leq 2$ or $alpha(g)geq n-3$.

The number of Sidon sets and the maximum size of Sidon sets contained in a sparse random set of integers

A set A of non-negative integers is called a Sidon set if all the sums a1+a2, with a1 ≤ a2 and a1, a2 ∈ A, are distinct. A well-known problem on Sidon sets is the determination of the maximum possible size F (n) of a Sidon subset of [n] = {0, 1, . . . , n− 1}. Results of Chowla, Erdős, Singer and Turán from the 1940s give that F (n) = (1 + o(1)) √ n. We study Sidon subsets of sparse random sets...

Integers for the Number of Maximal Independent Sets in Graphs

Let G be a simple undirected graph. Denote by mi(G) (respectively, xi(G)) the number of maximal (respectively, maximum) independent sets in G. In this paper we determine the third and fouth largest value of mi(G) among all graphs of order n. Moreover, the extremal graphs achieving these values are also determined. Mathematics Subject Classification: 05C35, 05C69, 68R10