论文标题
$ 3 $ - 颜色$ p_t $ - 没有短奇数的免费图形
$3$-Colouring $P_t$-free graphs without short odd cycles
论文作者
论文摘要
对于任何奇数$ t \ ge 9 $，我们提供了一种解决$ 3 $颜色问题的多项式时间算法，如果存在一个$ 3 $ - 颜色的颜色，则在$ p_ {t} $中 - 颜色 - $ p_ {t} $ - 免费图形的奇数围栏至少$ t-2 $。特别是，我们的算法适用于$（p_9，c_3，c_5）$ - 免费图形，从而取得了进步，以确定$ 3 $ - 颜色的$ p_t $ - free图的复杂性，该图均以$ t \ ge 8 $开放。
For any odd $t\ge 9$, we present a polynomial-time algorithm that solves the $3$-colouring problem, and finds a $3$-colouring if one exists, in $P_{t}$-free graphs of odd girth at least $t-2$. In particular, our algorithm works for $(P_9, C_3, C_5)$-free graphs, thus making progress towards determining the complexity of $3$-colouring in $P_t$-free graphs, which is open for $t\ge 8$.
