# good edge labeling, edge labeling

## Good edge labeling and girth ★★

\begin{conjecture} Every graph with large girth has a good edge labeling. \end{conjecture} More specifically: there exists a constant $g$ such that every graph with girth at least $g$ has a good edge labeling.

Keywords: good edge labeling, edge labeling

## Good Edge Labelings ★★

Author(s): Araújo; Cohen; Giroire; Havet

\begin{question} What is the maximum edge density of a graph which has a good edge labeling? \end{question}

We say that a graph is \emph{good-edge-labeling critical}, if it has no good edge labeling, but every proper subgraph has a good edge labeling.

\begin{conjecture} For every $c<4$, there is only a finite number of good-edge-labeling critical graphs with average degree less than $c$. \end{conjecture}

Keywords: good edge labeling, edge labeling