# Labeling

## Graceful Tree Conjecture ★★★

Author(s):

**Conjecture**All trees are graceful

Keywords: combinatorics; graceful labeling

## Good Edge Labelings ★★

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

**Question**What is the maximum edge density of a graph which has a good edge labeling?

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

**Conjecture**For every , there is only a finite number of good-edge-labeling critical graphs with average degree less than .

Keywords: good edge labeling, edge labeling