几类平面图的分数染色

THE FRACTIONAL-COLORING OF SOME PLANAR GRAPHS

图G的一个分数染色是从G的独立集的集合ζ到区间[0,1]的一个映射c,使得对任意顶点x,都c(s)≥1,将此分数染色的值定义为 s∈ζc(s).图G的分数色数χf(G)是它的所有分数染色的值的有 s∈ζ,s.t.x∈S下确界.讨论了几类平面图的分数色数.

A mapping c from the collection ζ of independent sets of a graph G to the interval [0, 1] is a fractional_coloring if for every vertex x of G we have s∈ζ,s.t. x∈Sc(s)≥1. The value of a fractional_coloring c is s∈ζc(s). The fractional_chromatic number χ_f(G) of G is the infimum of the values of fractional_colorings of G. The fractional chromatic number of some planar graphs was given.