2022/06/02 by Lei Xu, Tao Feng, Xu, Lei +1 · 1 citation
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2206.00900
openalex publication_date 2022/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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∈\3,4,8,16\, χ'(PG(n,q))=(qn-1)/(q-1), which implies the existence of a parallelism of PG(n,q) for any odd integer n and q∈\3,4,8,16\.