From 18d58cb26a490f8c047f8418f4483fbaad4a7b20 Mon Sep 17 00:00:00 2001 From: Martin Mares Date: Sat, 16 Jan 2010 16:58:38 +0100 Subject: [PATCH] Fixed the definition of edge density in Chapter 3.1. (infimum replaced by supremum; maybe lim sup would be even better, but the difference does not matter in our applications) --- adv.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/adv.tex b/adv.tex index 2a81be3..6cab6b7 100644 --- a/adv.tex +++ b/adv.tex @@ -73,7 +73,7 @@ theory. \defn\id{density}% Let $G$ be a~graph and $\cal C$ be a class of graphs. We define the \df{edge density} $\varrho(G)$ of~$G$ as the average number of edges per vertex, i.e., $m(G)/n(G)$. The -edge density $\varrho(\cal C)$ of the class is then defined as the infimum of $\varrho(G)$ over all $G\in\cal C$. +edge density $\varrho(\cal C)$ of the class is then defined as the supremum of $\varrho(G)$ over all $G\in\cal C$. \thmn{Mader \cite{mader:dens}}\id{maderthm}% For every $k\in{\bb N}$ there exists $h(k)\in{\bb R}$ such that every graph -- 2.39.2