Category Problem of the day
An observation on edge densities of the union of isomorphic copies of a fixed graph
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 […]
Double counting
Double counting is a simple yet so powerful way to prove non-trivial theorems. Here, we present some applications of the double counting principle. Our main source is the excellent book “Extremal Combinatorics” by Stasys Jukna [1]. A newer edition from the one in the picture (which shows the book I have) is also available now. […]
Fekete’s Lemma and an application on Ramsey theory
Fekete’s lemma was proved by Pólya and Szegő. A historical note, not related to Fekete’s lemma thought, which I did not know myself before reading the biography of Szegő and I find it for some reason interesting to know: At the age of 15, the young John von Neumann, recognised as a mathematical prodigy, was […]
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