This paper proves the following result. Assume
G is a triangle‐free planar graph,
X is an independent set of
G. If
L is a list assignment of
G such that
false|
L
(
v
)
false|
=
4 for each vertex
v
∈
V
(
G
)
−
X and
false|
L
(
v
)
false|
=
3 for each vertex
v
∈
X, then
G is
L‐colorable.
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