The L(2,1)-choosability‎ ‎of cycle

‎For a given graph G=(V,E)‎, ‎let \mathscr L(G)=\{L(v)‎ : ‎v\in V\} be a prescribed list assignment‎. ‎G is \mathscr L-L(2,1)-colorable if there exists a vertex labeling f of G such that f(v)\in L(v) for all v \in V; |f(u)-f(v)|\geq 2 if d_G(u,v) = 1; and |f(u)-f(v)| \geq 1 if d_G(u,v)=2‎. ‎If G is \mathscr L-L(2,1)-colorable for every list assignment \mathscr L with |L(v)|\geq k for all v\in V‎, ‎then G is said to be k-L(2,1)-choosable‎. ‎In this paper‎, ‎we prove all cycles are 5-L(2,1)-choosable‎.

کلیدواژه های The L(2,1)-choosability‎ ‎of cycle:

L(2 ، 1)-labeling ، Choosability ، cycle ، Path