  It is known that alternative links are pseudoalternating. In 1983 Louis
Kauffman conjectured that both classes are identical. In this paper we prove
that Kauffman Conjecture holds for those links whose first Betti number is at
most 2. However, it is not true in general when this value increases, as we
also prove by finding two counterexamples: a link and a knot whose first Betti
numbers equal 3 and 4, respectively.
