Graceful Tree Conjecture ★★★


\begin{conjecture} All trees are graceful \end{conjecture}

Keywords: combinatorics; graceful 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

Syndicate content