If G is a finitely presented
group and [Kscr ] is any (G,2)-complex (that is, a finite 2-complex with
fundamental group G), then it is well known that χ([Kscr ]) [ges ] ν(G),
where ν(G) = 1−rk H1G+dH2G. We
define χ(G) to be min{χ([Kscr ]): [Kscr ] a (G, 2)-complex}, and we say
that G is efficient if χ(G) = ν(G). In this
paper we give sufficient conditions for a Coxeter group to
be efficient (Theorem 4.2). We also give examples
of inefficient Coxeter groups (Theorem 5.1). In fact, we give
an infinite family Gn(n = 2, 3, 4, . . . ) of Coxeter
groups such that χ(Gn)−ν(Gn) [xrarr ] ∞ as n [xrarr ] ∞.