ON NONEXISTENCE OF SOME PERFECT 2-COLORINGS OF JOHNSON GRAPHS.
A perfect coloring in m colors of a graph G with matrix A = {aij}ij=1,...,m is a coloring of vertex set of G in the set of colors {1,..., m} such that the number of vertices of color j adjacent to a fixed vertex of color i does not depend on choice of the last vertex and equals aij. In this paper we obtain a low bound on parameter aij,i ≠ j, of a perfect coloring of a Johnson graph in two colors. Also we show that some perfect colorings of Johnson graph in two colors do not exist.