E-resources
Peer reviewed
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Zhu, Haiyang; Zhu, Junlei; Liu, Ying; Wang, Shuling; Huang, Danjun; Miao, Lianying
Journal of combinatorial optimization, 11/2022, Volume: 44, Issue: 4Journal Article
G has a list k - L (2, 1)-labeling if for any k -list assignment L , there exists a coloring c : V ( G ) → ⋃ v ∈ V L ( v ) of G such that c ( v ) ∈ L ( v ) for ∀ v ∈ V ( G ) and for ∀ u , v ∈ V ( G ) , | c ( u ) - c ( v ) | ≥ 2 if d ( u , v ) = 1 , | c ( u ) - c ( v ) | ≥ 1 if d ( u , v ) = 2 . λ 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 Δ ≥ 5 , girth g ≥ 13 and without adjacent 13-cycles, λ 2 , 1 l ( G ) ≤ Δ + 3 holds. Moreover, the upper bound Δ + 3 is tight.
