It is known that, for any k-list assignment L of a graph G, the number
of L-list colorings of G is at least the number of the proper k-colorings
of G when k>(mβ1)/ln(1+2β). In this paper, we extend the Whitney's
broken cycle theorem to L-colorings of signed graphs, by which we show that
if k>(3mβ)+(4mβ)+mβ1 then, for any k-assignment L, the
number of L-colorings of a signed graph Ξ£ with m edges is at least
the number of the proper k-colorings of Ξ£. Further, if L is 0-free
(resp., 0-included) and k is even (resp., odd), then the lower bound
(3mβ)+(4mβ)+mβ1 for k can be improved to
(mβ1)/ln(1+2β).Comment: 13 page