From 1091ad5cfcc9f0340345aac4aa25c5e7a1b0a7c0 Mon Sep 17 00:00:00 2001 From: Martin Mares Date: Sun, 20 Jan 2008 20:44:56 +0100 Subject: [PATCH] Notation. --- mst.tex | 2 +- notation.tex | 1 + 2 files changed, 2 insertions(+), 1 deletion(-) diff --git a/mst.tex b/mst.tex index 848d61a..8eb0baf 100644 --- a/mst.tex +++ b/mst.tex @@ -666,7 +666,7 @@ Non-trivial minor-closed classes include planar graphs and more generally graphs embeddable in any fixed surface. Many nice properties of planar graphs extend to these classes, too, most notable the linearity of the number of edges. -\defn +\defn\thmid{density}% Let $\cal C$ be a class of graphs. We define its \df{edge density} $\varrho(\cal C)$ to be the infimum of all~$\varrho$'s such that $\vert E(G) \vert \le \varrho\cdot\vert V(G)\vert$ holds for every $G\in\cal C$. diff --git a/notation.tex b/notation.tex index cd7f8dd..59552c9 100644 --- a/notation.tex +++ b/notation.tex @@ -26,6 +26,7 @@ \n{$G.e$}{simple graph contraction \[simpcont]} \n{$\alpha(n)$}{the inverse Ackermann's function} \n{$f[X]$}{function applied to a set: $f[X]:=\{ f(x) ; x\in X \}$.} +\n{$\varrho({\cal C})$}{edge density of a graph class~$\cal C$ \[density]} } \section{Multigraphs and contractions} -- 2.39.2