The chromatic index of finite projective spaces

Abstract

AbstractA line coloring of , the ‐dimensional projective space over GF, is an assignment of colors to all lines of so that any two lines with the same color do not intersect. The chromatic index of , denoted by , is the least number of colors for which a coloring of exists. This paper translates the problem of determining the chromatic index of to the problem of examining the existences of and with certain properties. In particular, it is shown that for any odd integer and , which implies the existence of a parallelism of for any odd integer and .