Geodesic
On nonexistence of some perfect 2-colorings of Johnson graphs
Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 5, pp. 52-68.

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A perfect coloring in $m$ colors of a graph $G$ with matrix $A=\{a_{ij}\}_{i,j=1,\dots,m}$ is a coloring of vertex set of $G$ in the set of colors $\{1,\dots,m\}$ 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 $a_{ij}$. In this paper we obtain a low bound on parameter $a_{ij}$, $i\neq j$, 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. Bibl. 13.
Keywords: perfect coloring, completely regular code, Johnson scheme. 
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I. Yu. Mogilnykh. On nonexistence of some perfect 2-colorings of Johnson graphs. Diskretnyj analiz i issledovanie operacij, Tome 16 (2009) no. 5, pp. 52-68. http://geodesic.mathdoc.fr/item/DA_2009_16_5_a5/

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