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- W3048310841 abstract "A list assignment of a graph G is a function (L: V(G)longrightarrow 2^{N}) that assigns each vertex v a list L(v) for all (vin V(G)). We say that G has an L-L(2, 1)-labeling if there exists a function (phi ) such that (phi (v)in L(v)) for all (vin V(G)), (|phi (u)-phi (v)|ge 2) if (d(u, v)=1) and (|phi (u)-phi (v)|ge 1) if (d(u, v)=2). The list L(2, 1)-labeling number of G, denoted by (lambda _{2,1}^{l}(G)), is the minimum k such that for every list assignment (L={L(v){:},|L(v)|=k, vin V(G)}), G has an L-L(2, 1)-labeling. We prove that for planar graph G with maximum degree (varDelta (G)) and girth g(G), (lambda _{2,1}^{l}(G)le varDelta (G)+3) holds if (varDelta (G)=4) and (g(G)ge 19) or (varDelta (G)=3) and (g(G)ge 32). Moreover, there exist planar graphs having (lambda _{2,1}^{l}(G)=varDelta (G)+3) for arbitrarily large (varDelta (G))." @default.
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- W3048310841 date "2020-01-01" @default.
- W3048310841 modified "2023-10-16" @default.
- W3048310841 title "The List L(2, 1)-Labeling of Planar Graphs with Large Girth" @default.
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- W3048310841 doi "https://doi.org/10.1007/978-3-030-57602-8_45" @default.
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