Résumé
A graph
G is
L-list colorable if for a given list assignment
L
=
{
L
(
v
)
:
v
∈
V
}
, there exists a proper coloring
c of
G such that
c
(
v
)
∈
L
(
v
)
for all
v
∈
V
. If
G is
L-list colorable for any list assignment with
|
L
(
v
)
|
⩾
k
for all
v
∈
V
, then
G is said
k-choosable. In [M. Voigt, A not 3-choosable planar graph without 3-cycles, Discrete Math. 146 (1995) 325–328] and [M. Voigt, A non-3-choosable planar graph without cycles of length 4 and 5, 2003, Manuscript], Voigt gave a planar graph without 3-cycles and a planar graph without 4-cycles and 5-cycles which are not 3-choosable. In this note, we give smaller and easier graphs than those proposed by Voigt and suggest an extension of Erdös' relaxation of Steinberg's conjecture to 3-choosability.