Consider a fixed graph with vertices and edges respectively. Assume that is balanced which means that the maximum edge density among all possible subgraphs of is achieved from $H$. Take two copies of , call them and create a new graph . In case the two copies are edge disjoint then the edge density of […]
A set of positive integers is said to have distinct sums (DS) if all sums where are distinct. We are interested in understanding the function . We obtain a simple lower bound on by observing that the set has DS as long as . Therefore, . Interestingly, this lower bound is not far away from being optimal, in […]
I just finished reading a short paper of Michael Krivelevich and Benny Sudakov, two leading experts in probabilistic combinatorics, which appeared in Arxiv about a month ago [1]. It is a simple proof of the classical result that the random binomial graph exhibits a phase transition around . When then the largest component has size […]
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