Independent sets in almost-regular graphs and the Cameron-Erdos problem for non-invariant linear equations

Abstract

We propose a generalisation of the Cameron-Erdos conjecture for sum-free sets to arbitrary non-translation invariant linear equations over Z in three or more variables and, using well-known methods from graph theory, prove a weak form of the conjecture for a class of equations where the structure of the maximum-size sets avoiding solutions to the equation has been previously obtained.

This paper is withdrawn as I have learned that the main result (Theorem 2.2) follows from a previously known result, namely Theorem 9.3 in the paper of Ben Green, "A Szemeredi-type regularity lemma in abelian groups, with applications", GAFA 15 (2005), 340-376