Achromatic number

Achromatic number — ахроматическое число.

The achromatic number [math]\displaystyle{ \,\psi(G) }[/math] of [math]\displaystyle{ \,G }[/math] is the maximum number of sets in a partition of [math]\displaystyle{ \,V }[/math] into independent subsets [math]\displaystyle{ V_{1}, V_{2}, \ldots, V_{k} }[/math] such that

(1) each [math]\displaystyle{ \,V_{i} }[/math] is an independent set of vertices, and

(2) for [math]\displaystyle{ i \neq j }[/math], there exists [math]\displaystyle{ v_{i} \in V_{i} }[/math] and [math]\displaystyle{ v_{j} \in V_{j} }[/math] such that [math]\displaystyle{ v_{i}v_{j} \in E(G) }[/math].