论文标题
平面图的奇数色数最多为8
The odd chromatic number of a planar graph is at most 8
论文作者
论文摘要
Petruševski and Škrekovski \cite{odd9} recently introduced the notion of an odd colouring of a graph: a proper vertex colouring of a graph $G$ is said to be \emph{odd} if for each non-isolated vertex $x \in V(G)$ there exists a colour $c$ appearing an odd number of times in $N(x)$. Petruševski和škrekovski证明，对于任何平面图$ g $，最多都有一种奇怪的颜色，最多使用$ 9 $颜色，并且与Caro \ cite {oddremarks}一起，表明$ 8 $的颜色足以容纳一个重要的平面图。我们表明，所有平面图的$ 8 $颜色就足够了。
Petruševski and Škrekovski \cite{odd9} recently introduced the notion of an odd colouring of a graph: a proper vertex colouring of a graph $G$ is said to be \emph{odd} if for each non-isolated vertex $x \in V(G)$ there exists a colour $c$ appearing an odd number of times in $N(x)$. Petruševski and Škrekovski proved that for any planar graph $G$ there is an odd colouring using at most $9$ colours and, together with Caro \cite{oddremarks}, showed that $8$ colours are enough for a significant family of planar graphs. We show that $8$ colours suffice for all planar graphs.
