论文标题
有限投影空间的色素指数
The chromatic index of finite projective spaces
论文作者
论文摘要
PG $（N，Q）$，GF $（Q）$的$ n $维投影空间的行着色是对所有PG $（N，Q）$的颜色的分配，因此具有相同颜色的任何两条线都不会相交。 PG $（N，Q）$的色度指数，用$χ'（PG（N，Q））$表示，是PG $（N，Q）$的颜色的最少颜色。本文将确定pg $（n，q）$的色度索引的问题转化为检查PG $（3，Q）$和PG $（4，Q）$具有某些属性的存在的问题。特别是，表明对于任何奇数整数$ n $和$ q \ in \ {3,4,8,16 \} $，$χ'（pg（n，q））=（q^n-1）/（q^n-1）$ $ q \ in \ {3,4,8,16 \} $。
A line coloring of PG$(n,q)$, the $n$-dimensional projective space over GF$(q)$, is an assignment of colors to all lines of PG$(n,q)$ so that any two lines with the same color do not intersect. The chromatic index of PG$(n,q)$, denoted by $χ'(PG(n,q))$, is the least number of colors for which a coloring of PG$(n,q)$ exists. This paper translates the problem of determining the chromatic index of PG$(n,q)$ to the problem of examining the existences of PG$(3,q)$ and PG$(4,q)$ with certain properties. In particular, it is shown that for any odd integer $n$ and $q\in\{3,4,8,16\}$, $χ'(PG(n,q))=(q^n-1)/(q-1)$, which implies the existence of a parallelism of PG$(n,q)$ for any odd integer $n$ and $q\in\{3,4,8,16\}$.
