G has a list k-L(2, 1)-labeling if for any k-list assignment L, there exists a coloring \(c:V(G)\rightarrow \bigcup \limits _{v\in V} L(v)\) of G such that \(c(v)\in L(v)\) for \(\forall v\in V(G)\) and for \(\forall u,v\in V(G)\), \(|c(u)-c(v)|\ge 2\) if \(d(u,v)=1\), \(|c(u)-c(v)|\ge 1\) if \(d(u,v)=2\). \(\lambda _{2,1}^{l}(G)=\min \{k|G\) has a list k-L(2, 1)-labeling\(\}\) is called the list L(2, 1)-labeling number of G. In this paper, we prove that for planar graph with maximum degree \(\Delta \ge 5\), girth \(g\ge 13\) and without adjacent 13-cycles, \(\lambda _{2,1}^{l}(G)\le \Delta +3\) holds. Moreover, the upper bound \(\Delta +3\) is tight.

ģ具有列表ķ -大号（2，1） -标号如果对于任何ķ -list分配大号，存在着色\（C：V（G）\ RIGHTARROW \ bigcup \限制_ {V \在V} L（ v）的\）的ģ使得\（C（v）的\在L（v）\）为\（\的forall v \在v（G）\）和\（\的forall U，v \在v（G )\) , \(|c(u)-c(v)|\ge 2\)如果\(d(u,v)=1\) , \(|c(u)-c(v)|\ ge 1\)如果\(d(u,v)=2\)。\(\lambda _{2,1}^{l}(G)=\min \{k|G\)有一个列表k - L (2, 1)-labeling \(\}\)称为列表L (2, 1) - G 的标记数。在本文中，我们证明对于最大度数\(\Delta \ge 5\)，周长\(g\ge 13\)且没有相邻 13圈的平面图，\(\lambda _{2,1}^ {l}(G)\le \Delta +3\)成立。此外，上限\(\Delta +3\)是紧的。