# r-graph

## Seymour's r-graph conjecture ★★★

Author(s): Seymour

An $r$-\emph{graph} is an $r$-regular graph $G$ with the property that $|\delta(X)| \ge r$ for every $X \subseteq V(G)$ with odd size.

\begin{conjecture} $\chi'(G) \le r+1$ for every $r$-graph $G$. \end{conjecture}

Keywords: edge-coloring; r-graph