  Buchstaber invariant is a numerical characteristic of a simplicial complex,
arising from torus actions on moment-angle complexes. In the paper we study the
relation between Buchstaber invariants and classical invariants of simplicial
complexes such as bigraded Betti numbers and chromatic invariants. The
following two statements are proved. (1) There exists a simplicial complex U
with different real and ordinary Buchstaber invariants. (2) There exist two
simplicial complexes with equal bigraded Betti numbers and chromatic numbers,
but different Buchstaber invariants. To prove the first theorem we define
Buchstaber number as a generalized chromatic invariant. This approach allows to
guess the required example. The task then reduces to a finite enumeration of
possibilities which was done using GAP computational system. To prove the
second statement we use properties of Taylor resolutions of face rings.
